Improved machine learning classifiers combined with a stochastic local search for Web services classification

Abstract

The Web services classification is the process that automatically assigns a category from a list of predefined categories to the Web service described as a WSDL document and where the purpose is to improve the Web services discovery process speed. The aim of this paper is to propose an optimization approach based on the attributes selection of Web services descriptions, to automatically classify Web services found in UDDI registers in predefined categories. The proposed approach combines the meta-heuristic of Stochastic Local Search (SLS) with a supervised learning method. The purpose of this work is to optimize the classification rate of the classifier by choosing the relevant attributes that best represents the Web service. First, we propose a classification method that uses a stochastic local search (SLS) for the attributes selection, then, in a second phase, the approach calls for a supervised classification method to perform the classification task. To this end, we studied six well-known classifiers which are: Support Vector Machine (SVM), Naïve Bayes (NB), $k$ -Nearest Neighbors ( $k$ -NN), Bayesian Network (BN), Random Tree (RT), and Random Forests (RF). The six hybrid methods which are: SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS are evaluated on seven real datasets. The results are interesting and demonstrate the benefits of the proposed approaches for Web service classification.

Keywords

Web services classification Support Vector Machine (SVM)Naïve Bayes (NB)k-Nearest Neighbors (k-NN)Bayesian Network (BN)Random Tree (RT)Random Forests (RF)Stochastic Local Search (SLS)Cross Validation features selection meta-heuristic optimization

1. Introduction

In recent years, Web services have emerged as a new Web technology, designed specifically to create efficient and effective software environments capable of managing data on the Web. This technology is mainly based on Service-Oriented Architecture (SOA) [30]. OASIS the Organization for the Advancement of Structured Information Standards gives the following definition of SOA [30]: “A paradigm for organizing and utilizing distributed capabilities that may be under the control of different ownership domains. It provides a uniform means to offer, discover, interact with and use capabilities to produce desired effects consistent with measurable preconditions and expectations”. In general, a service-oriented architecture consists of three fundamental concepts [30] namely, service provider: is an organization that provides the service, such an entity that provides a specific implementation of service; service requester: is an entity that seeks and calls a special service to achieve its objectives; and service registry: it is an entity that acts as a directory of services.

Web services are protocols and standards for communication and data exchange between applications in heterogeneous environments. According to the definition of the international standardization organization for Web technologies W3C definition (World Wide Web Consortium) [1, 7]: “A Web service is a software system designed to support interoperable machine-to-machine interaction over a network. It has an interface described in a machine-processable format (specifically WSDL). Other systems interact with the Web service in a manner prescribed by its description using SOAP messages, typically conveyed using HTTP with an XML serialization in conjunction with other Web-related standards.”. The Web services are associated with a set of XML (eXtensible Markup Language) specifications [7] namely, XML [11] (eXtensible Markup Language): It is used to describe documents and data in a standard format that can be easily transported via standard Internet protocols; SOAP [10] (Simple Object Access Protocol): Is a protocol that ensures the transport of data and communication infrastructure (XML document); WSDL [14] (Web Service Description Language): Is an XML document that specifies the description of the services offered; UDDI directory [15] (Universal Description Discovery and Integration): Is a specification for the description (the reference) and discovery of Web services.

Web services have become one of the most advanced technologies used on the Web, resulting in a sharp increase in its number and with different qualities. This continuous and important increase in the number of Web services makes it difficult to control and manage this huge amount of services, whether by service providers in the implementation phase or maintenance of Web services or by customers (service users) in the case of searching or invoking a particular service.

Every day, many Web services are published and updated by the providers. Moreover, important quantities of these services are searched and invoked on by consumers. The exponential growth of the needs of providers and consumers on the one hand and the large number of available Web services and publishing in the directories on the other hand requires a sophisticated and efficient automatic tool or mechanism to classify and organize these large quantities of Web services in categories.

Specifically, a Web Service is a set of features described in a WSDL document, specifying the methods to invoke, their signature, and the path of the service. These services are accessible via the SOAP protocol. In view of the huge amount of WSDL document descriptions of Web services available and accessible today on the Web, so it becomes necessary to find effective solutions to automatically categorize these quantities in predefined domains.

The Web services classification is a very important task, which involves assigning to a document (typically WSDL) one or more categories from a predefined list (supervised classification). More precisely, it is a process that allows to automatically sort a set of WSDL documents and categorize them. This process necessarily involves the study and exploration of WSDL documents that describe the services offered by Web services. The relevant classification of all Web services is a very difficult problem given the time constraints and the large number of documents to be processed. The classification of Web services is one methodology that can be used to improve the speed of Web services discovery and invocation processes. In general, the combination of different methods (algorithms) allows to get additional advantages to avoid the limitation of a single method. To this end, the classification of Web services by domain can be very useful to facilitate the services invocation. In this paper, we present an approach combining both a supervised machine learning method and an attribute selection technique for the classification of Web services.

Attributes selection is a difficult and complex process that eliminates redundant attributes and keeps only those deemed useful for classification, according to a certain evaluation function. Eliminating redundant attributes and preserving the relevant attributes will reduce the dataset size and significantly increase the performance and efficiency of classifiers (in terms of accuracy rate). It is therefore important to establish a powerful and efficient algorithm to find the optimal set of attributes. On the other hand, the Stochastic Local Search meta-heuristic (SLS) is one of the most important techniques used in the field of attribute selection [26, 27]. In this paper, we focus on the classification of Web services using the SLS meta-heuristic. We intend to use SLS as an attributes selection technique (the relevant attributes) from the WSDL document.

The main objective of this work is to propose a supervised classification system enhanced with a Stochastic Local Search (SLS). We use the SLS meta-heuristic for features selection and the supervised classifier for the classification task.

The SLS method consists in iteratively (recursively) selecting a relevant subset of attributes (the good subset of attributes that represents the optimal solution) of dimension $m$ from an attributes initial set of dimension $n$ where $m<n$ . The optimal subset of attributes necessarily leads to a better classification rate. The optimal subset of attributes selected by the meta-heuristic SLS (generated solution) will then be sent to the classifier according to the considered and reduced data (the new data corresponding to the optimal attribute subsets) in order to find the best classification rate. This mechanism is repeated until satisfying a stopping criterion.

In this paper, we study six well-known supervised machine learning methods such as: Support Vector Machine (SVM), Naïve Bayes (NB), $k$ -Nearest Neighbors ( $k$ -NN), Bayesian Network (BN), Random Tree (RT), and Random Forests (RF). These classifiers are combined with SLS (i.e. the six proposed approaches: SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS) and applied to the Web services classification problem. More precisely, the use of the SLS meta-heuristic for selecting attributes before starting the classification task is intended to select only a subset of significant attributes for the various machine learning methods. This may reduce the dataset size and enhance the accuracy rate. The performance of the six proposed approaches is evaluated with the 10-fold Cross Validation method and validated on seven real datasets of Web services available on the Web: QWS Dataset with 364 Web services divided into four categories (Platinum, Gold, Silver, Bronze) and the six versions of OWLS-TC ver. 2.2 (Text, OntImp, SynSig, SemSig, TextSynSig, and TextSemSig) with 1007 Web services divided into seven categories (Travel, Economy, Education, Food, Communication, Medical, Weapon).

The rest of this paper is structured as follows: In Section 2, the presentation of some related works. The definition of the Web services classification problem is given in Section 3. Section 4 presents the six machine learning algorithms, the SLS meta-heuristic, and the $k$ -fold Cross Validation method. The six proposed approaches based on SLS for solving the Web services classification problem are presented in Section 5. Section 6 gives the experiments and the obtained results. Finally, the conclusion of the proposed study and some perspectives are presented in Section 7.

2. Related works

In recent years, much effort has gone into developing automatic methodologies and approaches for classifying Web services in their application domain. In this section, we give an overview of the different approaches that exist in the literature.

Garofalakis et al. [20] presented an in-depth critical study on the solutions, methods, architectures, models and mechanisms of discovery and localization of Web services (i.e. locating and selecting a WSDL description of the service) found in the repositories (UDDI registry), as well as concerns raised during the process of Web services discovery. More specifically, the study aimed to examine and analyze the different approaches and mechanisms for discovering Web services based on different architectural perceptions (architectural aspects, standards and platforms). This study presented some promising solutions for developing discovery mechanisms for Web services (Besides the UDDI registry), which are: the semantic techniques based on Peer to Peer (P2P), the discovery mechanisms based on the grid and the information retrieval (IR) techniques. In addition, they presented some approaches based on ontologies where the objective was to improve data models. Some interesting solutions based on semantic Web technology were also discussed in this study.

In [16], the authors proposed the AWSC hybrid system (Automatic Web Service Classifier) to classify Web services based on their description. The system is a combination of machine learning methods and Text Mining techniques, whose purpose is to exploit the connections between the information found in the standard description of the Web service and its category (class of membership). In that work, three machine learning methods were used: Rocchio, Naïve Bayes, and $k$ -NN. The empirical evaluations on a set of 235 Web services have shown that when using Rocchio with TF-IDF, AWSC has a good performance compared to the results when using $k$ -NN and Naïve Bayes.

The authors in [46] presented a Web services classification system using association rules (AR) that aim to find an association relationship between the WSDL description and the Web services category. Their approach consists of two main steps: the first step is the preprocessing of WSDL documents using Text Mining techniques, and the second step is to use an automatic machine learning method to classify the documents into categories. According to their results the Naïve Bayes classifier has demonstrated more efficiency than the classifier based on association rules.

In [51], the authors developed a hierarchical classification approach for Web services based on the functional characteristics of a set of medium and large categories. They used as sample data the descriptive information of the sub-categories. Their approach uses as a classification method: Support Vector Machine (SVM) based on UNSPSC (United Nations Standard Products and Services Code) taxonomy as criteria for classification. The experimental results demonstrated the effectiveness and usefulness of the SVM method for the Web services classification.

Mohanty et al. [31] proposed a comparative study of seven well-known automatic machine learning methods: SVM, Group Method of Data Handling (GMDH), ID3 Decision tree (J48), TreeNet, Back Propagation Neural Network (BPNN), Classification and Regression Trees (CART), and Probabilistic Neural Network (PNN) to predict the quality of a Web service based on a number of QoS service quality attributes. The experiments were carried out on a QWS Dataset with 10 fold cross-validation. The average accuracy for different classifiers seems to be high and some classifiers give very high accuracies. Moreover, they applied a method of selecting a subset of set characteristics (with and without WSRF). They found that the following attributes (Without WSRF) are the most important: (Reliability, Throughput, Successability, Response time, and Documentation). In the same context, the previous authors presented in another study [32], an automatic approach based on the Bayesian network, which uses the Naïve Bayes classifier (NBC), the Markov blanket technology (MB) and the Tabu search meta-heuristic (TS) to classify Web services into categories. The results in terms of accuracy rate on the QWS Dataset (with and without WSRF) show that Naïve based Bayesian network performs better than other technologies.

Another method for Web services classification based on automatic semantic annotation and ensemble learning has been proposed in [54], the method applies an automatic semantic annotation of Web service and uses three supervised classification algorithm such as: Naïve Bayes, SVM and REPTree. In addition, the ensemble learning (AdaBoost, in abbr. AB) is applied. According to the experiment carried out on 951 WSDL files and 19 categories with 10-cross validation, the accuracy of the AdaBoost ensemble learning was the best compared to the other classifiers.

Vaadaala et al. proposed in [48] a system to predict the quality of Web services based on the J48 decision tree. The considered services are based on the set of QoS (Quality of Service) attributes of the QWS Dataset. This system uses the WsRF attribute (Web service Relevance Function) as the Web services classification criterion. Their experimental results show the effectiveness of the J48 method.

In [9], the authors defined an approach (HGCA: Hyper-graph Classification Algorithm) based on conceptual graphs in an unsupervised learning technique for classifying Web services. The conceptual graph is represented as a hyper-graph that identifies and constructs functional domains and also helps classify Web services in these areas (the terms of a WSDL document are considered as conceptual nodes). According to the authors, the use of conceptual graphics aims to achieve a high classification rate, which reduces the time to search for specific Web services.

A semantic method for the automatic classification of Web services was presented in [47]. The proposed method is based on a lexical semantic network built from extracts of the Web as a knowledge base to calculate the semantic similarity between the profile of a service and the categories. The method is composed of two phases: the analysis of service classification profiles, and the mapping of the profiles of services to category based vectors of dimension. Their method uses a standardized unsupervised similarity calculation approach combined with the TF-IDF weighting metric and weight generation techniques based on IR (Information Retrieval). The empirical evaluation on the OWL-S service set shows that this approach helps to make better decisions for a relevant classification of services by giving an ordered set of categories based on similarity scores.

Mustafa et al. [33], elaborated a comparative study of four classification methods (SVM, $k$ -NN, Fuzzy Rule Induction Algorithm Unordered (FURIA), and RIDOR) to examine the performance of Web services classifiers, their study is based on the QWS Dataset with nine attributes used to measure and predict the quality of service. According to their results, the average accuracy of the classification methods is considered to be high. In addition, the classification accuracy is improved with SVM-SMO training of (6.84%) compared to $k$ -NN and (3.48%) compared to RIDOR.

Another study [40] proposed an automatic approach based on three automatic learning methods for Web services classification using the standard QWS Dataset. The three considered classifiers are: Fuzzy Rough Ownership Nearest Neighbor (FRONN), Fuzzy Nearest Neighbor (FNN), and Rough Fuzzy Nearest Neighbor (FRNN). In their approach the Weighted Average Accuracy technology (WAA) was applied to the confusion matrix after the selection of attributes (FS techniques: Information Gain (IG) and Gain Rate (GR)) to improve the accuracy rate.

In [6], the authors discussed the work of several prominent researchers in the field of improving the performance and efficiency of the discovery mechanism of Web services (Web services available in the UDDI registry) using techniques based on machine learning models. In this study, the authors classified some existing approaches according to the mode of machine learning technique used (i.e. supervised mode, semi supervised, and unsupervised). More specifically, machine learning techniques on WSDL documents are widely used for Web service discovery problems. In addition, semantics and clustering can improve the process of discovering web services. According to the authors, the study is useful for Web service publishers to determine the appropriate Web service discovery mechanism and for consumers to obtain the required Web service.

The authors in [38] described a Text Mining technique for the classification of Web services in specific fields based on the following WSDL document features: Service name (SN), Service documentation (SD), WSDL schema (WSDLS), WSDL messages (WSDLM) and WSDL port types (WSDLP). The authors have proposed a system which consists of three components: WSDL Feature Extractor, Text Pre-processor, and Web Service Classifier. The approach is validated on a dataset of 600 Web services classified into 8 categories (with a classification rate of 90.6%). According to their experiences, the quality of the information retrieved has been improved compared to comparison approaches.

In [53], Yang et al. developed a semi-automatic Web services classification process based on four learning algorithms (SVM, Naïve Bayes, C4.5, and Back Propagation Neuron Network (BPNN)). The process is composed of four steps which are: the choice of the classification element among the WSDL document elements, the preprocessing of the data, the digital representation of the vector, and the application of the classifier. In their work, the selected WSDL elements are: service name, operation name, input/output, and a combination of the service name and the operation name, input and output. According to their experiences, they found that the C4.5 had a better accuracy.

An automatic machine learning approach for the Web services classification based on Multi-Layer Perceptron optimized with Tabu Search (MLP-TS) was described by [34]. The approach is compared with two models: Multi-Layer Perceptron-Levenberg-Marquardt (MLP-LM) and Multi-Layer Perceptron Back Propagation (MLP-BPP). The experimental results tested on the QWS Dataset show that the proposed MLP-TS is more efficient than MLP-LM and MLP-BPP.

The authors in [35], proposed an optimized model (MLP-GA) based on the MLP classification method with the back propagation to classify the instances of Web services, and the genetic algorithm (GA) to optimize the MLP classifier. In their study the authors use three classification techniques: Naïve Bayes, MLP-BPP and MLP-GA. The three techniques are evaluated on the QWS Dataset. The experimental results of the three classifiers compared to each other show the efficiency of the optimized (MLP-GA) model compared to MLP-BPP and Naïve Bayes.

In [43], the authors presented an automated approach for the classification of Web services into functionally similar categories. The approach is based on a set of majority votes of a combination of three conventional and heterogeneous classification techniques (the ensemble of classifiers: Naïve Bayes, SVM and Decision Tree (J48)) whose aim is to overcome the limits of these techniques. This approach is validated on a data set of 3738 real Web services classified in 5 domains, with an average accuracy of (92%). According to the authors, the results found are due to two main factors, namely: enhanced pre-processing with focused feature selection, and majority based ensemble classification (MEC).

A hybrid approach called (SVM $+$ SLS) for the supervised classification of Web services was presented in [26]. The approach combines a Support Vector Machine (SVM) algorithm and a meta-heuristic method of SLS for the selection of relevant attributes. The numerical results on QWS Dataset have proven the effectiveness and usefulness of the proposed approach. In another study, the same authors [27] proposed a hybrid approach to the supervised classification of Web services, which aims to improve the performance and effectiveness of the disaster management system, in order to reduce the damage and the risks caused by disasters. The approach is a combination of the Naïve Bayes classifier and the Stochastic Local Search (SLS), SLS is used for the selection of good attributes that reduce the attribute space and increases the performance of the NB classifier, in order to facilitate the Web services invocation in case of emergency or disaster by the competent authorities. The approach was evaluated on the QWS Dataset and gave good results in terms of classification rates.

Table 1
Related works approaches for Web services classification

Id	Author	Year	Proposed approach	Datasets	Mode
1	Garofalakis et al. [20]	2006	Investigative study	–	–
2	Crasso et al. [16]	2008	AWSC	235 WS	Supervised
3	Sharma et al. [46]	2010	Association rules	165 WS	Supervised
4	Wang et al. [51]	2010	SVM classifier	OWLS-TC	Supervised
5	Mohanty et al. [31]	2010	Intelligent techniques	QWS Dataset	Supervised
6	Mohanty et al. [32]	2012	Bayesian network	QWS Dataset	Supervised
7	Yuan-jie et al. [54]	2012	AdaBoost (AB)	951WS	Supervised
8	Vaadaala et al. [48]	2013	JForty Eight (J48)	QWS Dataset	Supervised
9	Boujarwah et al. [9]	2013	HGCA	OWLS-TC3	Unsupervised
10	Sharma et al. [47]	2014	Semantic similarity	OWLS-TC v2	Supervised
11	Mustafa et al. [33]	2014	SVM-SMO	QWS Dataset	Supervised
12	Patro et al. [40]	2015	FS techniques	QWS Dataset	Supervised
13	Bhardwaj et al. [6]	2015	Comparative study	–	–
14	Nisa et al. [38]	2015	Text Mining (TM)	600 WS	Supervised
15	Yang et al. [53]	2015	C4.5	OWLS-TC4	Supervised
16	Mustafa et al. [34]	2015	MLP $+$ TS	QWS Dataset	Supervised
17	Mustafa et al. [35]	2016	MLP-GA	QWS Dataset	Supervised
18	Qamar et al. [43]	2016	MEC	3738 WS	Supervised
19	Laachemi et al. [26]	2016	SVM $+$ SLS	QWS Dataset	Supervised
20	Laachemi et al. [27]	2017	NB $+$ SLS	QWS Dataset	Supervised
21	Zhu et al. [56]	2018	CNBP approach	QWS Dataset	Supervised
22	Shafi et al. [45]	2018	Maximum Entropy (ME)	OWLS-TC3	Supervised
23	Purohit et al. [42]	2019	Majority Vote (MV)	QWS Dataset	Supervised
24	Zhao et al. [55]	2019	ServeNet	10184 WS	Supervised

In [56], Zhu et al. presented a hybrid algorithm called CNBP (Cuckoo-Nelder-Mead-Back-Propagation) to efficiently classify candidate Web services into different quality of service (QoS) levels. The hybrid algorithm is an optimized back-propagation (BP) neural network with a hybrid of two algorithms: the Cuckoo search algorithm and the Nelder-Mead simplex algorithm. The CNBP algorithm optimizes the initial weights and biases of the BP neural network (BP classifier is used for the classification). The experiments conducted on the QWS Dataset and comparative analysis with the traditional BP network and three other supervised classification methods (SVM, NB, $k$ -NN), led to the conclusion that the CNBP approach is more efficient and stable for classification than other methods used in the comparison (i.e. CSBP algorithm, BP, SVM, NB, and $k$ -NN).

Shafi et al. [45], proposed an improved Web services classification technique based on text mining. The technique exploits the WSDL file contents, more precisely the service name and operations. They use the following three classifiers: Naive Bayes, C4.5 and Maximum Entropy (ME). The comparison results show that the Maximum Entropy gives the best solution for classification.

Another study [42] investigated the role of Web services in the Internet of Things and Smart Cities, specifically, with an emphasis on classification techniques. In their study, the authors used the Majority Vote (MV) method as a learning model for the supervised classification of Web services and compared it to six other models (LR, NNge, J48, MLP, RF, and JRip). The empirical results on the QWS Dataset show that the Majority Vote method improves the results of the classification according to the error rates: AAE and ARE.

In [55], Zhao et al. presented a new deep neural network called ServeNet (in abbreviation SN) for the Web services classification, this network automatically abstracts the low-level representation of the Web service description into high-level entities without feature engineering, and then predicting the service classification for 50 categories of services. The ServeNet is trained and tested on a dataset of 10184 Web services classified into 50 categories. The accuracy obtained is respectively (99.83% and 88.40%) in the top-5 on training and test set. The results found show that the deep neural network ServeNet is robust and can achieve the best performance (greater accuracy) compared to other machine learning methods.

Table 1 summarized the related works approaches for Web services classification.

3. Formulation of problem: The classification of Web services

The classification of Web services is a difficult problem given the large number of documents to be processed. The main objective of this study is to improve the efficiency and performance of classifiers (more specifically, the classification rate) in order to facilitate the task of service providers during the publication phase or in the case of service maintenance, and service customers (or service requesters) when searching for a particular service to invoke it. In other words, our main purpose of this study is to increase the performance of activities (such as: publication, discovery, and service invocation) that connects the three basic concepts of the SOA system [30] (Service provider, Service requester, Service registry). For this purpose, we are interested in this study to the problem of the Web services supervised classification. The problem of the Web services supervised classification is an automatic process that allows us to find or build an effective and efficient model capable of assigning a set of documents $d=\{d_{1},d_{2},\ldots,d_{n}\}$ (more precisely, WSDL documents) represented by a set of attributes or features to one or more classes among a set of classes $c=\{c_{1},c_{2},\ldots,c_{k}\}$ (a set of categories). In general, the supervised classification of Web services into predefined domains or classes is the operation of structuring and organizing Web services published in directories or registers of Web services (UDDI).

By definition [44], the supervised classification of Web services is a predictive technique of machine learning consists in examining the attributes (or characteristics) representing a document $d_{i}(x_{1},x_{2},\ldots,x_{n})$ of $n$ attributes (according to the characteristics extracted from the WSDL document) newly presented in order to assign it to a class among a set of predefined classes $c=\{c_{1},c_{2},\ldots,c_{k}\}$ . Before starting the classification process, an important step (the WSDL document pre-processing) is to process the WSDL documents using the Text Mining techniques in order to select the relevant attributes from the contents of the document WSDL. The operation of the classification is done in a process consisting essentially of two basic steps [44, 16]:

•
Construction of the classification model: the model is based on a set of training data with labels (training set).
•
Using the classification model: to classify new WSDL documents into predetermined classes with the test set.

Algorithm 1 represents the general process of the Web services supervised classification.

Algorithm 1: The general process of classification

1:input: a document $d(x_{1},x_{2},\ldots,x_{n})$ of $n$ attributes;

2:input:a set of $k$ predetermined classes $c=\{c_{1},c_{2},\ldots,$

$c_{k}\}$ ;

3:The classification model, Validation method: 10-fold

Cross validation;

4:output: a predicted class $c_{i}\in c$ of the document $d$ ;

In the literature, there are several machine learning techniques for the supervised classification task, including: Support Vector Machine (SVM) [49], Naïve Bayes (NB) [19], $k$ -Nearest Neighbors ( $k$ -NN) [17], Neural Networks [22] and Decisions trees [12]. In this article, we are interested in the use of the meta-heuristic method of Stochastic Local Search (SLS) as a combinatorial optimization method for selecting the good attributes of the WSDL document, these attributes facilitate the task of classifying WSDL documents into predetermined categories. This meta-heuristic SLS will be combined with a supervised machine learning algorithm in order to improve the classification rate and reduce the attribute space to facilitate the tasks of the main actors of the SOA system (publication, discovery, and invocation of Web services).
4. Background

Algorithm 1: The general process of classification
1:input: a document $d(x_{1},x_{2},\ldots,x_{n})$ of $n$ attributes;
2:input:a set of $k$ predetermined classes $c=\{c_{1},c_{2},\ldots,$
$c_{k}\}$ ;
3:The classification model, Validation method: 10-fold
Cross validation;
4:output: a predicted class $c_{i}\in c$ of the document $d$ ;

In this section, we briefly describe some of the important elements and concepts used in the proposed approaches, such as: the six machine learning algorithms, SLS (Stochastic Local Search), and $k$ -fold Cross Validation method.

4.1 Machine learning algorithms (supervised classification methods)

In this study, six well-known supervised machine learning methods, Support Vector Machine (SVM), Naïve Bayes (NB), $k$ -Nearest Neighbors ( $k$ -NN), Bayesian Network (BN), Random Tree (RT), and Random Forests (RF) were used. A brief introduction to these methods is presented in this subsection.

4.1.1 Support Vector Machine (SVM)

Support Vector Machine (SVM) is a very popular class of supervised machine learning algorithms developed by Vapnik in 1995 to solve classification and regression problems [49]. Moreover to its solid mathematical base, SVM is considered one of the most efficient and powerful algorithms in many real-world domains, such as: bioinformatics, handwriting recognition, object recognition, facial recognition, and large-scale classification problems such as the categorization of images and texts [23]. SVM is based on two fundamental ideas: the notion of kernel function and the concept of maximum margin. The basic principle of the SVM method is to create a hyper-plane separating the data into two classes in the case of binary classification and into several classes in the case of multi-class classification (i.e. $k$ classes), using the principle of maximum margin. In a binary classification, the SVM method attempts to separate the positive examples from the negative ones in the set of examples. The method then looks for the hyper-plane that separates the positive examples from the negative ones, ensuring that the margin between the nearest positive and negative examples is maximal (the search for an optimal hyper-plane). The classification of a new example is given by its position with respect to the optimal hyper-plane (i.e. see the sign of the decision function $f(x)$ ). The kernel function allows optimal separation data.

Let’s consider that this a classification problem with two classes, a negative class ( $-$ 1) and a positive class ( $+$ 1) represented by the following dataset: $D=(x_{1},y_{1}),\ldots,(x_{l},y_{l})$ , $y_{i}\in\{-1,+1\}$ , $i=1,{\dots},l$ where $\{(x_{i},y_{i})\}$ , $i=1,{\dots},l$ are the features vectors (the attributes) and $y_{i}\in\{-1,+1\}$ , $i=1,{\dots},{l}$ are the corresponding classes.

If the dataset is completely linearly separable, the separating hyper-plane into two classes with the largest margin can be written as follows:

$\displaystyle w.x+b=0,w\in\mathbb{R}^{n}\text{ et }b\in\mathbb{R}$ (1)

Where $x$ is an arbitrary point, $w$ is a weight vector and $b$ is the bias (scalar). The following formula represents the conditions for a better classification:

$\displaystyle\left\{\begin{array}[]{l}w.x_{i}+b\geqslant 1\text{ if }y_{i}=+1% \\ w.x_{i}+b\leqslant 1\text{ if }y_{i}=-1\\ \end{array}\right.$ (2)

Which is equivalent to:

$\displaystyle y_{i}(w.x_{i}+b)-1\geqslant 0\,\forall i\in\{1,\dots,l\}$ (3)

The margin is the distance of the nearest point to the hyper-plane, mathematically defined by the following formula:

$\displaystyle M=\frac{{2}}{||w||}$ (4)

Where $||w||$ is the Euclidean norm of $w$ . Finding the hyper-plane amounts to maximizing the margin $M$ , which is equivalent to the problem of minimizing a quadratic objective function with linear constraints according to:

$\displaystyle\left\{\begin{array}[]{l}\min\frac{1}{2}||w||^{2}\\ y_{i}(w.x_{i}+b)\geqslant 1\,\forall i\in\{1,\dots,l\}\\ \end{array}\right.$ (5)

The solution to the problem of convex quadratic optimization under linear constraints of Eq. (4) is given by the Lagrangian $L$ .

$\displaystyle L(w,b,\alpha)=\frac{1}{2}||w||^{2}-\sum^{l}_{i=1}{{\alpha}_{i}(y% _{i}(w.x_{i}+b)-1)}$ (6)

Where the $\alpha_{i}$ are the Lagrange multipliers associated with the constraints. The Lagrangian $L$ must be minimized with respect to $w$ , $b$ and maximize with respect to the variables $\alpha_{i}\geqslant 0$ . The Lagrangian $L(w,b,\alpha)$ is minimized with respect to $w$ :

$\displaystyle\frac{\partial L(w,b,\alpha)}{\partial w}=0\Longleftrightarrow w-% \sum^{l}_{i=1}{{\alpha}_{i}y_{i}x_{i}}=0$ (7)

The Lagrangian $L(w,b,\alpha)$ is minimized with respect to $b$ :

$\displaystyle\frac{\partial L(w,b,\alpha)}{\partial b}=0\Longleftrightarrow% \sum^{l}_{i=1}{{\alpha}_{i}y_{i}}=0$ (8)

Leading to the following solution:

$\displaystyle\left\{\begin{array}[]{l}w=\sum^{l}_{i=1}{{\alpha}_{i}y_{i}x_{i}}% \\ \sum^{l}_{i=1}{{\alpha}_{i}y_{i}}=0\\ \end{array}\right.$ (9)

The Lagrangian $L(w,b,\alpha)$ is maximized with respect to $\alpha\geqslant 0$ . By replacing Eq. (9) in the Eq. (6) of Lagrange $L(w,b,\alpha)$ , the dual problem equivalent to maximize is obtained according to:

$\displaystyle\text{max}_{\alpha}(Q(\alpha))=\text{max}_{\alpha}$ (10) $\displaystyle\left(\sum^{l}_{i=1}{{\alpha}_{i}}-\frac{1}{2}\sum^{l}_{i=1}\sum^% {l}_{j=1}{\alpha}_{i}{\alpha}_{j}y_{i}y_{j}(x_{i},x_{j})\right)$

Under the following constraints:

$\displaystyle\left\{\begin{array}[]{l}\sum^{l}_{i=1}{{\alpha}_{i}y_{i}=0}\\ {\alpha}_{i}\geqslant 0,i=1,\dots,l\\ \end{array}\right.$ (11)

This problem can be solved using quadratic programming methods. The optimal solution ${\alpha}^{*}=({\alpha}^{*}_{1},\dots,{\alpha}^{*}_{l})$ is obtained. The weight vector $w^{*}$ of the maximum margin hyper-plane is written as follows:

$\displaystyle w^{*}=\sum^{l}_{i=1}{{\alpha}^{*}_{i}y_{i}x_{i}}$ (12)

The associated decision function can be written in the following form:

$\displaystyle f(x)=w^{*}.x+b^{*}=\textit{sgn}\left(\sum^{l}_{i=1}{\alpha}^{*}_% {i}y_{i}x_{i}.x+b^{*}\right)$ (13)

A kernel function is a function $k(x_{i},x_{j})$ (the transformation kernel), where

$\displaystyle k(x,y)=\Phi{(x_{i})}^{T}\Phi(x_{j})$ (14)

The radial basis function kernel, or RBF kernel, is one of the most used kernel functions in supervised classification, especially for the SVM method. The RBF kernel takes the following form (Where, $\gamma>0$ is the kernel parameter):

$\displaystyle k(x_{i},x_{j})=e^{-\gamma||x_{i}-x_{j}||^{2}}$ (15)

4.1.2 Naïve Bayes (NB)

The Naïve Bayes method [19] is a supervised learning algorithm widely used for classification problems (i.e. classifying a set of observations according to defined rules), and more particularly used for text classification problems. It is a simple classification algorithm of the probabilistic classifiers family based on the Bayes theorem. This theorem is based on conditional probabilities with strong independence between the different attributes (A set of conditional independence hypotheses). In simple terms, a Naïve Bayes classifier assumes that the existence of a characteristic for a class is independent of the other characteristics existence. Assuming that $m$ classes $C=(C_{1},C_{2},\ldots,C_{m})$ is disposed (available). Let $X=(X_{1},X_{2},\ldots,X_{n})$ be a vector of $n$ attributes which must be classified and $C_{k}$ is the class of this vector. It is necessary to determine the probability ( $P(C_{k}|X)=P(C_{k}|X_{1},\ldots,X_{n})$ ) of belonging of the vector $X$ to the class $C_{k}$ . The following Bayes theorem is used to determine this probability:

$\displaystyle P(C_{k}|X_{,}\dots,X_{n})=\frac{P(C_{k})P(X_{1},\dots,X_{n}|C_{k% })}{P(X_{1},\dots,X_{n})}$ (16)

Where $P(X|C_{k})$ is the probability that, for a given category, the attributes of the vector $X$ are associated with the category $C_{k}$ . $P(C_{k})$ is the probability that associates the attribute vector $X$ with the category $C_{k}$ independently of the content of the document. $P(X)$ is the clean probability of the attributes vector $X$ . More generally, when $X$ contains $n$ attributes which satisfy the hypothesis of conditional independence, the probability $P(X_{1},{\dots},X_{n}|C_{k})$ is written as follows:

$\displaystyle P(X_{1},\dots,X_{n}|C_{k})=P(X_{1}|C_{k})*\dots*P(X_{n}|C_{k})$ (17)

Which is equivalent to:

$\displaystyle P(X_{1},\dots,X_{n}|C_{k})=\prod^{n}_{i=1}P(X_{i}|C_{k})$ (18)

Where $X_{i}$ represents the $i^{\text{th}}$ element of the attribute vector $X$ . By combining Eqs (16) and (18), the following formula (The Bayes theorem) is obtained:

$\displaystyle P(C_{k}|X_{1},\dots,X_{n})=\frac{P(C_{k})\prod^{n}_{i=1}{P(X_{i}% |C_{k})}}{P(X_{1},\dots,X_{n})}$ (19)

As the objective is to find the maximum of the probability $P(C_{k}|X)$ according to the class $C_{k}$ , And that $P(X)$ does not depend on $C_{k}$ . The hypothesis Maximum A Posteriori (MAP) can be used (The most likely class) the assignment rule below is found (i.e. Assign to $X$ the class $C_{k}$ such that $P(C_{k}|X)$ is maximal):

$\displaystyle C_{\textit{MAP}}\!\leftarrow\textit{argmax}_{(C_{k}\in C)}P(C_{k% })\prod^{n}_{i=1}P(X_{i}|C_{k})$ (20)

4.1.3 k-Nearest Neighbors (k-NN)

The $k$ -Nearest Neighbors ( $k$ -NN) classification method [17] is a supervised learning algorithm, based on instances dedicated to classification where each instance is characterized by a set of attributes used when calculating the distance. The method does not include a training phase, it uses two parameters: the number $k$ of nearest neighbors and the similarity function to compare the new case with the others that are already classified. To identify the class of a new instance (document), the $k$ -NN calculates its similarity with all instances already classified. Then, it places the values of similarity (distance) in descending order and keeps only the first $k$ . The most common class among these $k$ instances is the one that is assigned the new instance (the majority class is obtained with the following formula):

$\displaystyle\textit{Majority Voting}:y^{\prime}=\textit{argmax}_{c}\sum_{(x_{% i},y_{i})\in D_{z}}{fi(c=y_{i})}$ (21)

Where $c$ is a class label, $D_{z}$ its nearest neighbor list, $z=({x^{\prime}},{y^{\prime}})$ is the test object $y_{i}$ is the class label for the $i^{\text{th}}$ nearest neighbors, and $f i$ is an indicator function that returns the value “1” if its argument is True and “0” otherwise, and, $x$ represents the data of a training object, while $y$ is its class. Likewise, $x_{i}$ represents the test object data and $y_{i}$ is its class. The $k$ -NN is based on the notion of similarity [17], the distance used is of major importance so that it is calculated between the coordinates of two points $X=(x_{1},x_{2},\ldots,x_{n})$ and $Y=(y_{1},y_{2},\ldots,y_{n})$ . Among the distance measurements used are:

The Euclidean distance: This is a geometric distance in a multidimensional space, which calculates the square root of the sum of the square differences between the coordinates of two points. The Euclidean distance between points $X$ and $Y$ is defined as:

$\displaystyle\textit{Distance}_{\textit{Eucl}}(X,Y)=\sqrt{\sum^{n}_{i=1}{{(x_{% i}-y_{i})}^{2}}}$ (22)

The Manhattan distance: It is the sum of the absolute values of the differences between the coordinates of two points. Between two points $X$ and $Y$ , the Manhattan distance is defined by:

$\displaystyle\textit{Distance}_{\textit{Manh}}(X,Y)=\sum^{n}_{i=1}{|x_{i}-y_{i% }|}$ (23)

The Minkowski distance: It is a metric of general distance. Between two points $X$ and $Y$ , the Minkowski distance is calculated as:

$\displaystyle\textit{Distance}_{\textit{Mink}}(X,Y)=\left(\sum^{n}_{i=1}|x_{i}% -y_{i}|^{p}\right)^{1/p}$ (24)

For $p=$ 1, it is the distance from Manhattan and for $p=$ 2, it is the Euclidean distance.

4.1.4 Bayesian Network (BN)

The Bayesian Network (BN) [41] is an interesting and powerful technique in machine learning, based on a graphical description of random variables. Specifically, it represents a conditional independence between a set of variables. A Bayesian network $B=(G,\Theta)$ is defined by [41]: a directed acyclic graph (DAG) without circuit $G=({X},{E})$ consists of nodes and arcs, whose nodes are associated with a set of random variables ${X}=\{X_{1},X_{2},\ldots,X_{n}\}$ , and the dependency relations between the variables are represented by oriented arcs (E). Each variable $X_{i}$ (a node of the graph) is represented by a conditional probability table (based on parent values) that is determined using the Bayes theorem (Eq. (16)). The set of probabilities $\Theta=\{\theta_{1},\theta_{2},\ldots,\theta_{n}\}$ represents the probability distributions set of each node $X_{i}$ . It is defined as follows:

$\displaystyle{{\theta}}_{i}=P(X_{i}|Pa(X_{i}))$ (25)

Where $Pa(X_{i})$ is the set of nodes connected to ( $X_{i}$ ) by end arcs ( $X_{i}$ ) (i.e. the parent nodes of $X_{i}$ in the graph $G$ ). The joint probability distribution of the set of $X$ variables can be calculated by the following mathematical formula:

$\displaystyle P(X_{1},\dots,X_{n})=\prod^{n}_{i=1}P(X_{i}|Pa(X_{i}))$ (26)

4.1.5 Random Tree (RT)

The Random Tree (RT) is a supervised automatic classification algorithm belonging to the families of decision tree algorithms with a hierarchical representation in the form of a tree with a root node for access to the tree that subsequently divides in branches [12]. More precisely a random tree is a set of classification rules. Each internal node of the random tree corresponds to an attribute, and each terminal node (or leaf) corresponds to a class. Moreover, an individual to be classified is described by a set of variables, which are tested in the internal nodes and decisions are made in the terminal nodes of the tree. The final classification decisions of the individuals to be classified are specified at the level of the terminal nodes. In general, the random tree is a randomly generated tree from a set of decision trees with a number of random properties on each node (i.e. a stochastic process). Furthermore, the combination of large random trees sets leads to a model called random forest.

4.1.6 Random Forest (RF)

A Random Forest (RF) is a very powerful and very fast supervised learning method (set of a classifier) developed by Leo Breiman [13] using many decision tree models (i.e. an overall classifier composed of several decision trees). Moreover, Random Forests are a highly efficient prediction technique belonging to the classification and regression algorithm class [13]. More specifically, a Random Forest is a set of decision trees formed from the random selection of the training data samples. The term random was introduced into the process of creating random trees for the first time by: [13]. Thus, the set of Random Trees obtained is called Random Forest. Leo Breiman defined the Random Forest as follows [13]: “A random forest is a classifier consisting of a collection of tree structured classifiers $\{h(x,\theta_{k}),k=1,\ldots\}$ where the $\{\theta_{k}\}$ are independent identically distributed random vectors and each tree casts a unit vote for the most popular class at input x”. The estimate of the random forest is obtained by calculating the estimates average of the different trees of the forest (i.e. the result of the classification is simply determined by a majority vote).

4.2 Optimization with the SLS meta-heuristic

Meta-heuristics have been used in many areas such as combinatorial optimization. Finding good quality solutions (optimal solutions) to difficult combinatorial optimization problems is not an easy task from algorithmic point of view. In general, an optimization can be considered as a problem of minimization or maximization (i.e. the search for minimum or maximum values achievable in reasonable computing time and without guaranteeing feasibility or optimality). By definition [39], a combinatorial optimization problem consists in finding the maximum $s$ (or the minimum) $s^{*}$ of an application $f$ (a function to optimize or objective function or cost function), or $f\in\mathbb{N}$ , ${\mathbb{R}}$ , on a finite set $S$ such that $f(s^{*})=\text{max}_{s\in S}f(s)$ (or $f(s^{*})=\text{min}_{s\in S}f(s)$ ). In other words, a combinatorial optimization problem consists in finding an optimal solution $s^{*}\in S$ that minimizes or maximizes (optimizes) the value of the objective function $f$ .

According to the definition of Voss et al. [50]: “A meta-heuristic is an iterative master process that guides and modifies the operations of subordinate heuristics to efficiently produce high-quality solutions. It may manipulate a complete (or incomplete) single solution or a collection of solutions at each iteration. The subordinate heuristics may be high (or low) level procedures, or a simple local search, or just a constructive method.”. Many meta-heuristic algorithms for combinatorial optimization based on the attributes selection exist in the literature. Among these meta-heuristics are the Stochastic Local Search (SLS). SLS is a method based on neighbor search that has been successfully applied to several optimization problems [26, 27, 37, 8]. The SLS or iterative improvement method is a single-solution meta-heuristic belonging to local search methods that starts with an initial solution generated randomly. Then, the method tries to improve this solution iteratively by looking for a better solution in the current neighborhood. More specifically, the method explores the search space to find more solutions (the solutions are generated iteratively. i.e. solution $X_{i+1}$ solution is determined from solution $X_{i}$ ). The method combines diversification and intensification strategies to explore efficiently the search space and find a better solution.

•
First phase (diversification): randomly choose a nearby solution. It is applied with a fixed probability $w p$ (walk probability) $>$ 0. This probability is fixed empirically.
•
Second phase (intensification): choose the best neighbor solution. This phase is applied with a probability $p=1-wp$ .

In general, intensification and diversification strategies play a complementary role. A good combination of these two main (component) strategies will generally ensure that optimality is achievable. The search process of the optimal solution Sol is repeated for an empirically fixed number of iterations called (max_iteration). In this paper, we are interested in SLS for the selection of the right attributes to find the optimal subset with the best possible accuracy for the purpose of classifying Web services into predefined categories. The main steps of the SLS meta-heuristic are shown in Algorithm 2.

Algorithm 2: The Stochastic Local Search (SLS) meta-heuristic

1: include: Number of attributes (number_attributes);

2: include:Maximum number of iteration (max_iteration);

3: include:wp (walk probability) ${\in}$ [0, 1]; fitness $=$ Accuracy

rate;

4: Sol $\mathrm{\leftarrow}$ Randomly generate an initial solution Sol ( $a_{1}$ , $a_{2}$ ,

…, $a_{n}$ );

5: for ( $i=$ 1 to max_iteration) do

6: $r$ ${\leftarrow}$ random number ${\in}$ [0, 1] (generate a random $r\in$ [0,

1]);

7: if ( $r{>}$ wp) then

8: Pick a random neighbor solution: Generate

neighborhood Sol:

9: neighborhood (Sol);

10: Sol ${\leftarrow}$ the best solution in the neighborhood;

11: else

12: $a{\leftarrow}$ a random attribute ${\in}$ [1, number_attributes];

13: if (Sol [ $a$ ] $==$ 1) then

14: Sol [ $a$ ] ${\leftarrow}$ 1;

15: else

16: Sol [ $a$ ] ${\leftarrow}$ 0;

17: end if

18: end if

19: end for

20: return: The optimal solution Sol ( $a_{1},a_{2},\ldots,a_{n}$ );

4.3 Validation method: Cross validation

Algorithm 2: The Stochastic Local Search (SLS) meta-heuristic
1: include: Number of attributes (number_attributes);
2: include:Maximum number of iteration (max_iteration);
3: include:wp (walk probability) ${\in}$ [0, 1]; fitness $=$ Accuracy
rate;
4: Sol $\mathrm{\leftarrow}$ Randomly generate an initial solution Sol ( $a_{1}$ , $a_{2}$ ,
…, $a_{n}$ );
5: for ( $i=$ 1 to max_iteration) do
6: $r$ ${\leftarrow}$ random number ${\in}$ [0, 1] (generate a random $r\in$ [0,
1]);
7: if ( $r{>}$ wp) then
8: Pick a random neighbor solution: Generate
neighborhood Sol:
9: neighborhood (Sol);
10: Sol ${\leftarrow}$ the best solution in the neighborhood;
11: else
12: $a{\leftarrow}$ a random attribute ${\in}$ [1, number_attributes];
13: if (Sol [ $a$ ] $==$ 1) then
14: Sol [ $a$ ] ${\leftarrow}$ 1;
15: else
16: Sol [ $a$ ] ${\leftarrow}$ 0;
17: end if
18: end if
19: end for
20: return: The optimal solution Sol ( $a_{1},a_{2},\ldots,a_{n}$ );

Cross-validation [49] is a very popular statistical technique (a resampling procedure) that has been used by practitioners for many years to evaluate and estimate the skills of machine learning models on a limited sample of data. This technique divides the total available data into two sets: a training set to form the model and a test set to evaluate and test the model performance. Many variants of cross-validation exist in the literature. Among these variants is the $k$ -fold cross validation method. This method [5] has a single parameter $k$ (integer) which refers to the number of groups in which a given sample (dataset) must be divided. In this variant, the data is divided into $k$ subsets of the same size. Among the $k$ subsets, only one subset is retained as validation data to test the model and the other subsets ( $k$ -1) are gathered together to form a training set. The cross validation process is repeated $k$ times (choosing another subset as the validation set. The training data set is modified accordingly), with each of the $k$ subsets used exactly once as validation data. The results $k$ of the subsets can then be calculated on average to produce a single estimate. The error estimate in the $k$ -fold cross-validation method is averaged over all the tests to obtain the total model efficiency.

5. Proposed approaches

In this section, we propose a SLS meta-heuristic for the selection of good attributes. This meta-heuristic is associated with a machine-learning algorithm for classifying Web services to improve the classifier performance (i.e. the classification rate), and this can reduce the size of the dataset. For this purpose, six supervised learning algorithms belonging to different groups have been selected (functions: SVM, bayes: NB, lazy: $k$ -NN, bayes: BN, trees: RT, and trees: RF). The proposed approaches (SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS) have two main steps:

•
First step: The use of the SLS method for the relevant attributes selection.
•
Second step: The classification of Web services based on these relevant attributes using the six chosen learning algorithms.

The problem of attribute selection is a classic problem of combinatorial optimization difficult-to-solve belonging to the class of NP-hard problems [36, 21, 29, 18], because for $n$ attributes, the possible subsets are 2 ${}^{n}$ , so the selection of attributes is considered a combinatorial optimization problem. The attribute selection is a technique of selecting (searching for or choosing) a subset of relevant attributes of size $m$ from a set of $n$ attributes (the starting set of size $n>m$ ), such as the value of the objective function is optimized (maximized) for all subsets of size $m(m<n)$ whose purpose is to reduce the dataset to be studied this can reduce the processing time and improve the classification of the dataset instances. In general, the attribute selection can be modeled as a combinatorial optimization problem difficult to solve (NP-hard), hence the need to use a meta-heuristic. We propose using the SLS meta-heuristic for selecting the good attributes. The problem of selecting relevant attributes for the Web services classification can be considered as a combinatorial optimization problem of maximization ( $S$ , $f$ ) where $S$ is the combination of all relevant attributes and $f$ is the objective function (fitness). This maximization problem ( $S$ , $f$ ) is formulated as follows:

•
The set of possible solutions $S$ (the search space): represents the optimal subsets of the good attributes.
•
The objective function (fitness $f(s)f:S{\to}{\mathbb{R}}$ ): it corresponds to the function that needs to be optimized (i.e. ${\forall}s{\in}S$ , $f(s)$ represents the accuracy rate of a classifier built with the subset of attributes $s$ , the Accuracy rate is the percentage of examples correctly classified by the classifier).
•
The neighborhood of a solution $s$ : corresponds to solutions adjacent to $s$ , each solution being obtained randomly by a change of the current solution $s$ (either by the addition or the deletion of an entity from the attributes vector with size $n$ ).

The objective function of the maximization problem ( $S, f$ ) is defined as follows:

$\displaystyle\textit{fitness}=\textit{Accuracy rate}(\textit{Classification % rate})=\frac{tp+tn}{tp+tn+fp+fn}$ (27)

Section 6 describes in more detail the measures of performance evaluation of classifiers: Accuracy rate, Error rate, Precision, Recall, and F-Measure.

The main objective of this work is to optimize the classification rate (maximize) by selecting a subset of the best attributes (i.e. the optimal combinations of relevant attributes). The basic idea is to improve iteratively an existing solution by exploring a neighborhood. The neighboring solution that gives the maximum value of the classification rate (the maximum value returned by the objective function) among a set of possible neighboring solutions is selected and considered as a new current solution for the next iteration of the SLS meta-heuristic.
5.1 Stochastic Local Search (SLS) for attributes selection

The proposed approaches are hybridizations between a supervised classifier and a stochastic local search (SLS). The purpose of the SLS meta-heuristic is to iteratively select the subset of relevant attributes (the optimal solutions) in order to properly classify Web services. The selected attributes are sent to the classifier to find the best classification rate according to the value of the objective function. More specifically, SLS starts with an initial solution chosen in a random way and tries to improve it iteratively by looking for a better solution in the current neighborhood (i.e. Replace the current solution by one of its neighbors taking into account the objective function). All neighboring solutions are evaluated using the objective function. For this purpose, SLS uses two strategies to guide the search for solutions. Diversification that generate different solutions to explore large-scale research space, and intensification that focuses research on a local region to find the best current solution. SLS is repeated for a certain maximum number of iterations fixed empirically (max_iteration). The main steps of the SLS meta-heuristic have been presented in Algorithm 2 of Section 4.2.

5.2 The general form of a solution generated by SLS

A Web service is a set of attributes described in a WSDL document. This set represents a solution generated by the meta-heuristics SLS. In general, SLS requires an initial solution chosen randomly. Generally, for a set of data with $n$ attributes, there are 2 ${}^{n}$ possible subsets (i.e. 2 ${}^{n}$ combinations of possible attributes) to evaluate. A solution used in SLS for attribute selection is can be modeled by a binary vector (0, 1), where each bit represents an attribute. If an attribute is selected in a solution, its associated bit is set to 1, otherwise it is set to 0. As a result, the length of the solution vector is equal to the number of attributes indicating the attributes present in the dataset. The general form of a solution generated by SLS is given as follows: GenSol $=<a_{1},a_{2},\ldots,a_{n}>$ , where $a_{1},a_{2},\ldots,a_{n}{\in}\{0,1\}$ , and $n{\in}{\mathbb{N}}$ (the number of attributes in the dataset). Algorithm 3 presents a representation of a solution generated by SLS.

Algorithm 3: Representation of a solution generated by SLS
1: include: $n$ : integer (number of attributes in the dataset);
2: include: $a_{i}{\in}\{0,1\}$ : an attribute, GenSol $=<a_{1},a_{2},{\dots},$
$a_{n}>$ : binary array;
3: for ( $i=$ 1 to $n$ ) do
4: if ( $a_{i}$ selected) then
5: GenSol [ $i$ ] ${\leftarrow}$ 1;
6: else GenSol [ $i$ ] ${\leftarrow}$ 0;
7: end if
8: end for
9: return: GenSol $=<a_{1},a_{2},\ldots,a_{n}>$ : the final solution
generated by SLS;

For example, if $n=$ 10, the following binary string: GenSol $=$ “1001110010” represent a solution generated by SLS, GenSol is a set of 10 attributes meaning that the selected attributes are: the (1 ${}^{\text{st}}$ ), (4 ${}^{\text{th}}$ ), (5 ${}^{\text{th}}$ ), (6 ${}^{\text{th}}$ ), and (9 ${}^{\text{th}}$ ) (six attributes selected from a subset of ten attributes). In addition, the neighborhood solutions of the current solution GenSol $=$ “1001110010” are: {0001110010, 1101110010, 1011110010, 1000110010, 1001010010, 1001100010, 1001111010, 1001110110, 1001110000, 1001110011}.

5.3 The proposed optimization algorithm with SLS for attribute selection

The optimization approaches proposed to solve the Web services classification problem consists of combining two techniques, a supervised machine learning technique with a Stochastic Local Search (SLS). These approaches are validated with 10-fold cross validation. Algorithm 4 presents the main steps of the proposed approaches.

Algorithm 4: Proposed approach for Web services classification
1:	include: Data set scaling arff format, Number of attributes
	(number_attributes);
2:	Maximum number of execution (max_execution);
3:	Maximum number of iteration (max_iteration);
4:	$w p$ (walk probability) ${\in}$ [0, 1], $k$ : number of fold
	cross-validation;
5:	$k$ : number of fold cross-validation, SLS Meta-
	heuristic;
6:	fitness $=$ Accuracy rate evaluation by 10-cross
	validation;
7:	Supervised classifiers: SVM, NB, $k$ -NN, BN, RT, RF;
8:	Choose a classifier among the 6 supervised classifiers;
9:	Sol ${\leftarrow}$ GenSol ( $a_{1},a_{2},\ldots,a_{n}$ ): generated solution by SLS;
10:	for ( $i=$ 1 to max_execution) do
11:	Randomly generate an initial solution Sol;
12:	Accuracy ${\leftarrow}$ Call the supervised classifier with Sol;
13:	for ( $j=$ 1 to max_iteration) do
14:	$r{\leftarrow}$ random number ${\in}$ [0, 1] (generate a random $r{\in}$ [0,
	1]);
15:	if ( $r>wp$ ) then
16:	Pick a random neighbor solution: Generate
	neighborhood Sol:
17:	neighborhood (Sol);
18:	Sol ${\leftarrow}$ the best solution in the neighborhood;
19:	Accuracy ${\leftarrow}$ Call a supervised classifier with best sol;
20:	else
21:	$a{\leftarrow}$ a random attribute ${\in}$ [1, number_attributes];
22:	if (Sol [ $a$ ] $==$ 1) then
23:	Sol [ $a$ ] ${\leftarrow}$ 1;
24:	else
25:	Sol [ $a$ ] ${\leftarrow}$ 0;
26:	end if
27:	Accuracy $\bm{{\leftarrow}}$ Call a supervised classifier with Sol;
28:	end if
29:	end for
30:	end for
31:	return: Accuracy optimal of classification;

6. Experimental results

In this section, we present the experimental results obtained by the six approaches proposed (SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS) adapted to solve the Web services classification problem. The evaluation measures and more precisely the accuracy rate were obtained using a Cross-Validation by 10, which uses (9/10) of the dataset for learning the algorithms and the rest for the test phase.

Table 2
Implementation details for the proposed approaches

Id	Approach	Open source code of WEKA	Programming language	Operating system
Ap ${}_{1}$	SVM $+$ SLS	functions.libSVM	Java	Ubuntu Server
Ap ${}_{2}$	NB $+$ SLS	bayes.NaiveBayes	Java	Ubuntu Server
Ap ${}_{3}$	$k$ -NN $+$ SLS	lazy.IBk	Java	Ubuntu Server
Ap ${}_{4}$	BN $+$ SLS	bayes.BayesNet	Java	Ubuntu Server
Ap ${}_{5}$	RT $+$ SLS	trees.RandomTree	Java	Ubuntu Server
Ap ${}_{6}$	RF $+$ SLS	trees.RandomForest	Java	Ubuntu Server

Table 3

The best values of the parameters of the proposed approaches

Id	Parameters	Values
P ${}_{1}$	max_execution (Maximum number of execution)	30
P ${}_{2}$	max_iteration (Maximum number of iteration)	50
P ${}_{3.1}$	$wp_{(\text{SVM}+\text{SLS})}$ ${\in}$ [0, 1]: The walk probability of (SVM $+$ SLS) approach	0.6
P ${}_{3.2}$	$wp_{(\text{NB}+\text{SLS})}$ ${\in}$ [0, 1]: The walk probability of (NB $+$ SLS) approach	0.6
P ${}_{3.3}$	$wp_{({k}\text{-NN}+\text{SLS})}$ ${\in}$ [0, 1]: The walk probability of ( $k$ -NN $+$ SLS) approach	0.6
P ${}_{3.4}$	$wp_{(\text{BN}+\text{SLS})}$ ${\in}$ [0, 1]: The walk probability of (BN $+$ SLS) approach	0.6
P ${}_{3.5}$	$wp_{(\text{RT}+\text{SLS})}$ ${\in}$ [0, 1]: The walk probability of (RT $+$ SLS) approach	0.6
P ${}_{3.6}$	$wp_{(\text{RF}+\text{SLS})}$ ${\in}$ [0, 1]: The walk probability of (RF $+$ SLS) approach	0.6
P ${}_{4}$	$k$ : integer (Number of folds of cross-validation)	10
P ${}_{5}$	The objective function SLS: fitness	Accuracy rate
P ${}_{6}$	Other evaluation measures	Er, Pr, Re, and F-M
P ${}_{7}$	Data sets	{D ${}_{1}$ , D ${}_{2}$ , …, D ${}_{7}$ }

6.1 Implementation details

The algorithms of the proposed approaches have been implemented in Java with the Eclipse development environment (Java IDE Integrated Development Environment) under the operating system: Ubuntu Server 16.04.2 LTS (Xenial Xerus) and executed on the machine: Intel machine (R) Core (TM) i5 CPU 2.4 GHz with 4 GB of RAM. Moreover, the SLS method was implemented in Java language and inserted into the WEKA source codes of the various machine learning methods selected for this study [52]. The WEKA 3.8.2 simulator (Waikato Environment for Knowledge Analysis) (http://www.cs.waikato.ac.nz/ml/weka/) [52] is a machine learning software for data mining tasks (pretreatment, classification, regression, grouping, association rules and visualization) developed by the Waikato University, written in java language. The WEKA preprocess and analyze data in ARFF format (Attribute Relationship File Format) or CSV format (Comma-Separated Values). The implementation details for each approach are shown in Table 2.

6.2 The parameters of the proposed approaches (parameters tuning)

Several series of tests were carried out to fix the best values of the parameters of the proposed algorithms for the resolution of the Web services classification problem. The maximum number of executions (max_execution), the maximum number of iterations (max_iteration), the walk probability $w p$ (a fixed probability ${\in}$ [0, 1]), the number of folds of Cross-Validation $k$ , and, the objective function of the SLS meta-heuristic (fitness $=$ Accuracy rate) represent the parameters of the six approaches proposed in this paper. The first three parameters (P ${}_{1}$ : max_execution, P ${}_{2}$ : max_iteration, and P ${}_{3}$ : $w p$ ) are defined and fixed empirically, i.e. after an experimental study. We performed several experiments to find the best values of the proposed approaches parameters. The value of each parameter is shown in the Table 3.

The performance of the proposed approaches was evaluated by a 10-fold Cross-Validation, which is the standard way to measure the accuracy rate [5].

6.3 Data sets used in this study

The performance of these approaches is validated and tested on two real datasets: QWS Dataset [2, 3, 4] and the OWLS-TC ver. 2.2 collection [24, 25]. This latter consists of six different versions (Text, OntImp, SynSig, SemSig, TextSynSig, and TextSemSig). Table 4 provides a general description of the datasets used in the evaluation process (D ${}_{1}$ , D ${}_{2}$ , D ${}_{3}$ , D ${}_{4}$ , D ${}_{5}$ , D ${}_{6}$ , and D ${}_{7}$ ).

Table 4
The general description of QWS Dataset and the six versions of OWLS-TC ver. 2.2 [2, 24]

Id	Datasets	Attributes	Instances	Categories	Type	Format
D ${}_{1}$	QWS Dataset	10	364	4	Numeric	ARFF
D ${}_{2}$	Text	454	1007	7	Numeric	ARFF
D ${}_{3}$	OntImp	30	1007	7	Numeric	ARFF
D ${}_{4}$	SynSig	397	1007	7	Numeric	ARFF
D ${}_{5}$	SemSig	397	1007	7	Numeric	ARFF
D ${}_{6}$	TextSynSig	851	1007	7	Numeric	ARFF
D ${}_{7}$	TextSemSig	851	1007	7	Numeric	ARFF

6.3.1 The QWS Dataset benchmark

The QWS Dataset [2, 3, 4] it is a collection of 364 real Web services (available on the Web) classified in four categories (Platinum, Gold, Silver and Bronze). Each row of QWS Dataset represents a Web service and these nine corresponding QWS (Quality of Web Service) attributes. The classification in 4 classes of the quality of these Web services is measured by WsRF (Web service Relevance Function) parameter (i.e. the tenth attribute $a_{10}$ ) with the following attributes [2, 3, 4]: { $a_{1}$ : Response Time ( $m s$ ), $a_{2}$ : Availability (%), $a_{3}$ : Throughput (Invokes/second), $a_{4}$ : Successability (%), $a_{5}$ : Reliability (%), $a_{6}$ : Compliance (%), $a_{7}$ : Best Practices (%), $a_{8}$ : Latency (ms), $a_{9}$ : Documentation (%), $a_{10}$ : WsRF (%), and $y$ : Service Classification (Classifier)}. The detailed description of the QWS Dataset is presented in Table 5.

Table 5
The detailed description of QWS Dataset [2, 3, 4]

Categories of Web services	Number of Web services	Percentage of Web services
Category 1: Platinum (high quality)	41	11.26%
Category 2: Gold	100	27.47%
Category 3: Silver	120	32.97%
Category 4: Bronze (low quality)	103	28.30%
Total	364	100%

6.3.2 The OWLS-TC ver. 2.2 benchmark

The OWLS-TC ver. 2.2 [24, 25] is an artificial collection used in several research works on the Web services classification. It is composed of 1007 OWL-S advertisements pre-classified into seven classes: Travel, Education, Weapon, Food, Economy, Communication, and Medical. This collection is composed of six different versions of the dataset in WEKA format (.arff), namely: Text, OntImp, SynSig, SemSig, TextSynSig, and TextSemSig. Its detailed description is presented in Table 6.

Table 6
The detailed description of the OWLS-TC ver. 2.2 [24, 25]

Categories of Web services	Number of Web services	Percentage of Web services
Category 1: Travel	165	16.39%
Category 2: Economy	365	36.25%
Category 3: Education	274	27.21%
Category 4: Food	33	3.28%
Category 5: Communication	58	5.76%
Category 6: Medical	73	7.25%
Category 7: Weapon	39	3.87%
Total	1007	100%

6.4 Scaling of the benchmark (data sets)

Feature scaling (data normalization) [28] is a simple and important technique performed during the data preprocessing stage and applied before using the data in their raw form (i.e. the original data). Specifically, this technique is used to normalize the data in predetermined ranges and make them usable by the machine learning algorithms for the classification task. The technique consists in resizing the range of features (i.e. the values of the dataset attributes) to resize it in a range between [0, 1] or [ $-$ 1, 1] ([ $A$ , $B$ ] is the predefined interval of the feature scaling) whose purpose is to obtain smaller standard deviations, which makes it possible to avoid numerical difficulties during the calculation step and thus to avoid the effect of outliers. The normalization range selection depends essentially on the data nature. The main advantage of data normalization is that it preserves the relationships between the original data values. The general formula for the feature scaling is given as follows [28]:

$\displaystyle X^{\prime}=\left(\frac{X-\textit{Min}_{a}}{\textit{Max}_{a}-% \textit{Min}_{a}}\right)\times(B-A)+A$ (28)

Where $X^{\prime}$ refers to the original attribute value, $X$ refers to the attribute value to scaling, $\textit{Max}_{a}$ is the upper limit of the attribute value (a) and $\textit{Min}_{a}$ is the lower limit of the attribute value (a), $A$ and $B$ denote the minimum value and the maximum value of the predefined interval. In this study, we use $A=-$ 1 and $B=$ 1 for the minimum and maximum values of the predefined interval. As a result, Eq. (28) becomes [28]:

$\displaystyle X^{\prime}=\left(\frac{X-\textit{Min}_{a}}{\textit{Max}_{a}-% \textit{Min}_{a}}\right)\times 2-1$ (29)

6.5 Evaluation measures of classification performance

Evaluation measures play a major and important role in the design of classifiers. These measures are based on the confusion matrix, in order to evaluate and validate the performance of classification algorithms. To evaluate the results produced by the different algorithms, we use the following five evaluation measures: Accuracy rate, Error rate, Precision, Recall and F-Measure.

The accuracy rate (classification rate) is the percentage of examples correctly classified by the classifier. In this study, the accuracy rate is defined by:

$\displaystyle\textit{Accuracy rate}(\textit{classification rate})=\frac{tp+tn}% {tp+tn+fp+fn}$ (30)

The error rate is the percentage of examples misclassified. It is obtained by:

$\displaystyle\textit{Error rate}=\frac{fp+fn}{tp+tn+fp+fn}=1-\textit{Accuracy rate}$ (31)

The precision is the proportion of predicted positives which are actual positive. It is defined by:

$\displaystyle\textit{Precision}=\frac{tp}{tp+fp}$ (32)

The recall is the proportion of actual positives which are predicted positive. It is obtained by:

$\displaystyle\textit{Recall}=\frac{tp}{tp+fn}$ (33)

The F-Measure (F-score): harmonic mean of Precision and Recall. It is defined by:

$\displaystyle\textit{F-Measure}=2\times\left(\frac{\textit{Precision}\times% \textit{Recall}}{\textit{Precision}+\textit{Recall}}\right)$ (34)

Where $t p$ is the “true positive”, $t n$ is the “true negative”, $f p$ is the “false positive”, and $f n$ is the “false negative”. The diagonal elements $t p$ and $t n$ in the confusion matrix (Table 7) represent the data properly classified by the classifier while other $f n$ and $f p$ diagonal elements represent the misclassified data.

Table 7

A confusion matrix for a binary classification (2 classes)

		Predicted class
Real class		X	Y
	X	$t p$	$f p$
	Y	$f n$	$t n$

6.6 Results obtained and discussion

In this subsection, we present the results obtained from the six proposed optimization approaches applied to the seven datasets D ${}_{i}$ ( $i=1,\ldots,7$ ). Generally, these approaches are iterative processes that are repeated several times until the stopping criterion is reached. Each approach has been applied several times during a number of executions initially set (max_execution $=$ 30). Then, each execution is repeated several times during a number of iterations initially set (max_iteration $=$ 50). More precisely, each approach evaluated 1500 possible solutions (i.e. max_execution $\times$ max_iteration $=$ 30 $\times$ 50 $=$ 1500 possible solutions or 1500 possible subsets of attributes). For each subset of attributes Sol ${}_{i}$ (1 $\leqslant i\leqslant$ 50), the classifier gives the corresponding evaluation measures (fitness $=$ Accuracy rate Acc ${}_{i}$ , Error rate Er ${}_{i}$ , Precision Pr ${}_{i}$ , Recall Re ${}_{i}$ , and F-Measures F-M ${}_{i}$ ). Furthermore, among these 50 evaluation measures given by the classifier, the following values are calculated: The minimum accuracy (MIA %), the maximum accuracy (MAA %), the best accuracy (BA %), the best error rate (BER %), the best precision (BP), the best recall (BR), the best F-Measures (BFM), the number of relevant attributes (NA), and the calculation time in seconds (CT) for each execution Exe ${}_{j}$ (1 $\leqslant j\leqslant$ 30). More precisely, for each execution Exe ${}_{j}$ (1 $\leqslant j\leqslant$ 30), the classifier gives the following results: MIA ${}_{j}$ , MAA ${}_{j}$ , BA ${}_{j}$ , BER ${}_{j}$ , BP ${}_{j}$ , BR ${}_{j}$ , BFM ${}_{j}$ , NA ${}_{j}$ , and CT ${}_{j}$ . Then, the global averages of the following values: BA, BER, BP, BR, BFM, NA and CT are calculated with the following formula (Eq. (35)):

$\displaystyle\textit{Average}(X)=\textit{Mean}(X)=\frac{1}{\text{max}\_\textit% {execution}}\sum^{\text{max}\_\textit{execution}}_{i=1}{X_{i}}$ (35)

Where $X_{i}$ is {BA, BER, BP, BR, BFM, NA, and CT}.

In the following, the experimental results found of the six proposed approaches (the optimal solutions) validated on the seven datasets (i.e. 7 $\times$ 6 $=$ 42 possible results), according to the following evaluation measures: Accuracy rate, Error rate, Precision, Recall and F-Measure. Moreover, the following statistical measures were calculated for each data set: Min, Max, Q ${}_{1}$ (First quartile: is the median of the lower half of a data series), Med (Median: represents the intermediate number of a data series), Q ${}_{3}$ (Third quartile: is the median of the upper half of a data series), Mod (The most frequent value in a data series), SD (Standard Deviation $\sigma$ : is a measure of the numbers distribution), and Avg (see the Eq. (35)) for each evaluation measure.

Table 8 presents the optimal solutions (OP) found by the two proposed approaches {(Ap ${}_{1}$ : SVM $+$ SLS with the kernel RBF (Radial Basis Function) and the probability $wp_{(\text{SVM}+\text{SLS})}=$ 0.6) and Ap ${}_{2}$ : NB $+$ SLS with the probability $wp_{(\text{NB}+\text{SLS})}=$ 0.6)}.

Table 8

The optimal solutions (OP) for the two proposed approaches (Ap ${}_{1}$ : SVM $+$ SLS and Ap ${}_{2}$ : NB $+$ SLS)

Data set	OP	Optimal solutions of Ap ${}_{1}$ : SVM $+$ SLS						Optimal solutions of Ap ${}_{2}$ : NB $+$ SLS
		BA	BER	BP	BR	BFM	NA	BA	BER	BP	BR	BFM	NA
D ${}_{1}$	Min	84.34	1.10	0.855	0.843	0.845	1	85.16	0.55	0.856	0.852	0.851	1
	Q ${}_{1}$	85.37	2.54	0.865	0.854	0.855	1.25	87.64	3.64	0.878	0.875	0.874	2
	Med	87.09	12.91	0.883	0.871	0.872	3	89.70	10.30	0.905	0.897	0.897	5
	Q ${}_{3}$	97.46	14.63	0.976	0.975	0.975	6.75	96.36	12.36	0.964	0.964	0.964	7
	Mod	98.90	1.10	0.989	0.989	0.989	1	87.64	12.36	0.995	0.995	0.995	1
	Max	98.90	15.66	0.989	0.989	0.989	9	99.45	14.84	0.995	0.995	0.995	9
	SD	5.77	5.77	0.053	0.058	0.057	2.75	5.01	5.01	0.049	0.051	0.051	2.78
	Avg	90.48	9.52	0.911	0.905	0.905	4	91.58	8.42	0.918	0.916	0.915	4.77
D ${}_{2}$	Min	55.91	24.33	0.361	0.559	0.441	1	90.17	7.85	0.903	0.902	0.899	147
	Q ${}_{1}$	58.54	27.23	0.419	0.586	0.466	17.75	91.26	8.04	0.916	0.913	0.911	182.75
	Med	66.73	33.27	0.796	0.667	0.638	51.5	91.76	8.24	0.919	0.918	0.917	206.50
	Q ${}_{3}$	72.77	41.46	0.832	0.728	0.724	237.50	91.96	8.74	0.921	0.920	0.918	229.50
	Mod	56.60	43.40	0.843	0.566	0.459	1	91.96	8.04	0.919	0.920	0.919	185
	Max	75.67	44.09	0.843	0.757	0.758	430	92.15	9.83	0.923	0.922	0.920	453
	SD	7.32	7.32	0.197	0.073	0.122	156.63	0.51	0.51	0.004	0.005	0.006	82.75
	Avg	65.88	34.12	0.660	0.659	0.608	136.50	91.60	8.40	0.918	0.916	0.914	232.97
D ${}_{3}$	Min	72.59	20.95	0.677	0.726	0.683	6	60.08	26.12	0.575	0.601	0.550	3
	Q ${}_{1}$	76.07	21.85	0.737	0.761	0.725	12.25	64.05	30.14	0.714	0.641	0.651	8.25
	Med	78.05	21.95	0.800	0.781	0.768	15.5	65.84	34.16	0.738	0.658	0.667	10.50
	Q ${}_{3}$	78.15	23.93	0.824	0.782	0.776	20.75	69.86	35.95	0.743	0.699	0.703	14.75
	Mod	78.05	21.95	0.800	0.781	0.768	14	73.88	26.12	0.759	0.739	0.728	9
	Max	79.05	27.41	0.833	0.790	0.788	30	73.88	39.92	0.761	0.739	0.728	29
	SD	1.47	1.47	0.045	0.015	0.028	6.56	4.31	4.31	0.037	0.043	0.040	5.92
	Avg	77.31	22.69	0.787	0.773	0.755	16.6	66.82	33.18	0.726	0.668	0.669	11.87
D ${}_{4}$	Min	36.25	29.10	0.131	0.362	0.193	3	69.31	12.61	0.739	0.693	0.682	29
	Q ${}_{1}$	57.57	31.13	0.631	0.576	0.500	25.75	85.63	12.93	0.875	0.856	0.854	142
	Med	64.35	35.65	0.789	0.644	0.630	44.5	86.40	13.60	0.884	0.864	0.861	158.5
	Q ${}_{3}$	68.87	42.43	0.798	0.689	0.672	99.25	87.07	14.37	0.888	0.871	0.867	180.75
	Mod	70.90	29.10	0.797	0.709	0.696	37	87.29	12.71	0.884	0.873	0.868	153
	Max	70.90	63.75	0.828	0.709	0.696	393	87.39	30.69	0.891	0.874	0.869	397
	SD	10.25	10.25	0.207	0.103	0.151	101.53	3.44	3.44	0.030	0.035	0.036	63.26
	Avg	61.04	38.96	0.678	0.610	0.564	86.30	85.49	14.51	0.873	0.855	0.851	166.3
D ${}_{5}$	Min	72.29	15.89	0.694	0.723	0.682	27	85.50	10.53	0.869	0.855	0.853	238
	Q ${}_{1}$	80.56	16.58	0.835	0.805	0.796	115	87.91	11.42	0.881	0.879	0.877	339.50
	Med	82.22	17.78	0.843	0.822	0.812	134	88.28	11.72	0.886	0.883	0.883	355.50
	Q ${}_{3}$	83.42	19.44	0.851	0.834	0.823	155.75	88.58	12.09	0.891	0.886	0.885	369.75
	Mod	82.22	17.78	0.843	0.822	0.829	150	88.58	11.42	0.883	0.886	0.885	377
	Max	84.11	27.71	0.856	0.841	0.829	390	89.47	14.50	0.897	0.895	0.894	393
	SD	3.27	3.27	0.044	0.033	0.040	71.72	0.88	0.88	0.008	0.009	0.009	30.25
	Avg	81.27	18.73	0.830	0.813	0.799	150.47	88.11	11.89	0.885	0.881	0.880	349.70
D ${}_{6}$	Min	46.08	24.33	0.351	0.461	0.355	1	90.07	7.05	0.905	0.901	0.896	179
	Q ${}_{1}$	56.16	27.98	0.404	0.562	0.450	27	91.04	7.35	0.915	0.911	0.907	217.25
	Med	64.55	35.45	0.693	0.646	0.584	169.50	92.40	7.60	0.926	0.925	0.923	268.50
	Q ${}_{3}$	72.02	43.84	0.818	0.720	0.706	558.75	92.65	8.96	0.928	0.927	0.925	501.25
	Mod	66.34	33.66	0.403	0.663	0.622	249	90.07	9.93	0.929	0.901	0.924	225.00
	Max	75.67	53.92	0.846	0.757	0.755	848	92.95	9.93	0.930	0.929	0.929	850
	SD	10.12	10.12	0.199	0.102	0.146	309.46	0.99	0.99	0.008	0.010	0.011	214.44
	Avg	63.16	36.84	0.622	0.630	0.572	290.20	91.85	8.15	0.921	0.919	0.917	378.43
D ${}_{7}$	Min	67.43	14.20	0.619	0.674	0.617	20	80.54	6.75	0.809	0.805	0.803	91
	Q ${}_{1}$	78.03	14.52	0.824	0.781	0.772	166.75	92.55	6.95	0.928	0.926	0.923	582.75
	Med	85.15	14.85	0.861	0.852	0.840	187.50	92.95	7.05	0.930	0.929	0.928	734
	Q ${}_{3}$	85.48	21.97	0.864	0.855	0.844	291.75	93.05	7.45	0.932	0.930	0.929	795.50
	Mod	85.20	14.80	0.861	0.852	0.846	236	92.95	7.05	0.931	0.929	0.928	489
	Max	85.80	32.57	0.867	0.858	0.847	849	93.25	19.46	0.933	0.932	0.931	846
	SD	6.24	6.24	0.071	0.062	0.076	215.73	2.30	2.30	0.023	0.023	0.023	159.93
	Avg	81.25	18.75	0.821	0.813	0.794	269.70	92.32	7.68	0.925	0.923	0.921	663.67

Table 9

The optimal solutions (OP) for the two proposed approaches (Ap ${}_{3}$ : $k$ -NN $+$ SLS and Ap ${}_{4}$ : BN $+$ SLS)

Data set	OP	Optimal solutions of Ap ${}_{3}$ : $k$ -NN $+$ SLS						Optimal solutions of Ap ${}_{4}$ : BN $+$ SLS
		BA	BER	BP	BR	BFM	NA	BA	BER	BP	BR	BFM	NA
D ${}_{1}$	Min	79.67	0.27	0.803	0.797	0.799	1	99.45	0	0.995	0.995	0.994	1
	Q ${}_{1}$	84.21	6.04	0.851	0.842	0.843	2	100	0	1	1	1	2.25
	Med	87.36	12.64	0.876	0.874	0.874	4	100	0	1	1	1	4
	Q ${}_{3}$	93.96	15.80	0.942	0.940	0.940	5	100	0	1	1	1	6
	Mod	93.96	6.04	0.942	0.940	0.940	2	100	0	1	1	1	3
	Max	99.73	20.33	0.997	0.997	0.997	9	100	0.55	1	1	1	9
	SD	6.46	6.46	0.062	0.065	0.064	2.24	0.13	0.13	0.001	0.001	0.001	2.46
	Avg	89.52	10.48	0.899	0.895	0.896	3.77	99.95	0.05	1	1	1	4.43
D ${}_{2}$	Min	92.45	6.06	0.926	0.925	0.924	306	92.25	6.16	0.922	0.923	0.922	188
	Q ${}_{1}$	93.64	6.16	0.937	0.936	0.936	437	93.55	6.36	0.936	0.935	0.935	348.25
	Med	93.74	6.26	0.938	0.937	0.937	441.50	93.55	6.45	0.936	0.935	0.935	408
	Q ${}_{3}$	93.84	6.36	0.939	0.938	0.938	445	93.64	6.45	0.937	0.936	0.936	435.50
	Mod	93.74	6.26	0.941	0.937	0.937	444	93.55	6.45	0.936	0.935	0.935	346
	Max	93.94	7.55	0.941	0.939	0.939	453	93.84	7.75	0.939	0.938	0.938	453
	SD	0.33	0.33	0.003	0.003	0.003	31.35	0.27	0.27	0.003	0.003	0.003	56.04
	Avg	93.69	6.31	0.938	0.937	0.936	432.60	93.55	6.45	0.936	0.935	0.935	387.60
D ${}_{3}$	Min	78.45	20.26	0.817	0.785	0.787	10	57.30	34.06	0.400	0.573	0.461	1
	Q ${}_{1}$	79.64	20.26	0.824	0.796	0.794	14.25	64.72	34.16	0.725	0.647	0.646	8.25
	Med.	79.74	20.26	0.827	0.797	0.795	17	65.34	34.66	0.743	0.653	0.662	14.50
	Q ${}_{3}$	79.74	20.36	0.827	0.797	0.795	22.75	65.84	35.28	0.744	0.658	0.667	21.75
	Mod	79.74	20.26	0.827	0.797	0.795	16	65.94	34.06	0.744	0.659	0.668	14
	Max	79.74	21.55	0.827	0.797	0.795	29	65.94	42.70	0.763	0.659	0.668	29
	SD	0.24	0.24	0.002	0.002	0.001	5.46	2.15	2.15	0.088	0.021	0.051	8.32
	Avg	79.66	20.34	0.826	0.796	0.794	18.4	64.66	35.34	0.714	0.646	0.644	15
D ${}_{4}$	Min	87.19	8.24	0.883	0.872	0.871	72	90.27	9.24	0.907	0.903	0.901	201
	Q ${}_{1}$	90.27	8.84	0.906	0.903	0.901	358	90.57	9.26	0.908	0.906	0.902	370.25
	Med	90.27	9.73	0.907	0.903	0.902	368	90.57	9.43	0.909	0.906	0.903	373
	Q ${}_{3}$	91.16	9.73	0.916	0.912	0.912	384.75	90.74	9.43	0.911	0.908	0.905	377
	Mod	90.27	9.73	0.906	0.903	0.902	72	90.57	9.43	0.908	0.906	0.903	371
	Max	91.76	12.81	0.92	0.918	0.917	393	90.76	9.73	0.911	0.908	0.905	396
	SD	1.26	1.26	0.011	0.013	0.013	104.55	0.15	0.15	0.001	0.002	0.001	53.52
	Avg	90.24	9.76	0.907	0.903	0.902	333.87	90.59	9.41	0.909	0.906	0.903	357.33
D ${}_{5}$	Min	90.27	6.06	0.908	0.903	0.903	137	81.33	12.51	0.836	0.813	0.806	139
	Q ${}_{1}$	92.95	6.45	0.935	0.929	0.930	163.50	87.21	12.51	0.891	0.872	0.872	282
	Med	93.30	6.70	0.937	0.933	0.933	194.50	87.39	12.61	0.892	0.874	0.873	319
	Q ${}_{3}$	93.55	7.05	0.939	0.935	0.935	247	87.49	12.79	0.893	0.875	0.874	347.75
	Mod	93.55	6.45	0.939	0.933	0.933	201	87.49	12.51	0.892	0.875	0.874	345
	Max	93.94	9.73	0.943	0.939	0.939	394	87.49	18.67	0.893	0.875	0.874	396
	SD	0.75	0.75	0.007	0.007	0.007	81.78	1.12	1.12	0.010	0.011	0.012	54.37
	Avg	93.12	6.88	0.935	0.931	0.931	221.50	87.11	12.89	0.890	0.871	0.870	312.87
D ${}_{6}$	Min	93.05	6.75	0.932	0.930	0.929	775	93.35	5.76	0.934	0.933	0.932	453
	Q ${}_{1}$	93.15	6.85	0.933	0.931	0.930	821.25	94.04	5.86	0.941	0.940	0.940	619
	Med	93.15	6.85	0.933	0.931	0.930	828.50	94.04	5.96	0.941	0.940	0.940	625.50
	Q ${}_{3}$	93.15	6.85	0.933	0.931	0.930	835.75	94,14	5.96	0.942	0.941	0.940	730.75
	Mod	93.15	6.85	0.933	0.931	0.930	789	94.04	5.96	0.941	0.940	0.940	619
	Max	93.25	6.95	0.933	0.932	0.931	850	94.24	6.65	0.943	0.942	0.942	850
	SD	0.05	0.05	0.000	0.000	0.000	19.77	0.22	0.22	0.002	0.002	0.002	78.65
	Avg	93.17	6.83	0.933	0.931	0.930	825.07	94.02	5.98	0.941	0.940	0.940	658.10
D ${}_{7}$	Min	93.74	5.16	0.938	0.937	0.937	256	91.66	5.86	0.919	0.917	0.916	381
	Q ${}_{1}$	94.14	5.16	0.942	0.941	0.941	617.50	93.05	6.65	0.932	0.930	0.929	463.50
	Med.	94.59	5.41	0.947	0.946	0.946	654	93.35	6.75	0.934	0.933	0.932	501.50
	Q ${}_{3}$	94.84	5.86	0.949	0,948	0.948	685	93.35	6.95	0.934	0.933	0.933	776.75
	Mod	94.84	5.16	0.949	0.948	0.948	705	93.35	6.65	0.934	0.933	0.932	454
	Max	94.84	6.26	0.949	0.948	0.948	850	94.14	8.34	0.941	0.941	0.941	850
	SD	0.42	0.42	0.004	0.004	0.004	148.30	0.64	0.64	0.006	0.006	0.007	169.87
	Avg	94.45	5.55	0.945	0.944	0.944	627.53	93.14	6.88	0.932	0.931	0.930	610.63

Table 10

The optimal solutions (OP) for the two proposed approaches (Ap ${}_{5}$ : RT $+$ SLS and Ap ${}_{6}$ : RF $+$ SLS)

Data set	OP	Optimal solutions of Ap ${}_{5}$ : RT $+$ SLS						Optimal solutions of Ap ${}_{6}$ : RF $+$ SLS
		BA	BER	BP	BR	BFM	NA	BA	BER	BP	BR	BFM	NA
D ${}_{1}$	Min	94.51	0	0.946	0.945	0.945	1	100	0	1	1	1	1
	Q ${}_{1}$	96.77	0.89	0.968	0.968	0.968	4	100	0	1	1	1	4
	Med	97.53	2.47	0.976	0.975	0.975	6	100	0	1	1	1	6
	Q ${}_{2}$	99.11	3.23	0.991	0.991	0.991	7	100	0	1	1	1	7
	Mod	100	0	0.976	0.975	0.975	7	100	0	1	1	1	7
	Max	100	5.49	1	1	1	9	100	0	1	1	1	9
	SD	1.66	1.66	0.016	0.017	0.017	2.16	0	0	0	0	0	2.08
	Avg	97.66	2.34	0.977	0.977	0.977	5.47	100	0	1	1	1	5.73
D ${}_{2}$	Min	87.39	8.94	0.878	0.874	0.873	76	94.14	4.87	0.942	0.941	0.941	201
	Q ${}_{1}$	88.85	9.76	0.892	0.889	0.888	100.25	94.64	5.06	0.947	0.946	0.946	350.25
	Med	89.47	10.53	0.899	0.895	0.895	240.50	94.84	5.16	0.949	0.948	0.948	366
	Q ${}_{3}$	90.24	11.15	0.904	0.903	0.902	369.75	94.94	5.36	0.951	0.949	0.949	409.75
	Mod	88.38	11.62	0.904	0.884	0.902	354	94.64	5.36	0.947	0.946	0.946	360
	Max	91.06	12.61	0.912	0.911	0.910	453	95.13	5.86	0.952	0.951	0.951	453
	SD	0.93	0.93	0.009	0.009	0.009	140.90	0.22	0.22	0.002	0.002	0.002	50.87
	Avg	89.49	10.51	0.898	0.895	0.895	250.50	94.81	5.19	0.949	0.948	0.948	378.17
D ${}_{3}$	Min	78.35	20.36	0.816	0.784	0.786	10	79.44	20.06	0.830	0.794	0.792	11
	Q ${}_{1}$	79.64	20.36	0.825	0.796	0.795	12	79.84	20.06	0.830	0.798	0.797	14.25
	Med	79.64	20.36	0.825	0.796	0.795	15	79.84	20.16	0.830	0.798	0.797	18.50
	Q ${}_{3}$	79.64	20.36	0.825	0.796	0.795	20.75	79.94	20.16	0.832	0.799	0.798	22
	Mod	79.64	20.36	0.825	0.796	0.795	11	79.84	20,16	0.830	0.798	0.797	22
	Max	79.64	21.65	0.833	0.796	0.795	28	79.94	20.56	0.835	0.799	0.798	29
	SD	0.25	0.25	0.003	0.002	0.002	5.09	0.09	0.09	0.001	0.001	0.001	5.09
	Avg	79.56	20.44	0.825	0.795	0.794	16.33	79.87	20.13	0.831	0.798	0.797	18.70
D ${}_{4}$	Min	83.02	9.73	0.861	0.830	0.831	54	87.39	5.76	0.889	0.874	0.874	65
	Q ${}_{1}$	87.12	10.82	0.879	0.871	0.873	95.25	93.05	6.18	0.936	0.930	0.931	304.50
	Med	88.38	11.62	0.894	0.884	0.886	132	93.55	6.45	0.941	0.935	0.936	360
	Q ${}_{3}$	89.18	12.88	0.901	0.892	0.892	259	93.82	6.95	0.944	0.938	0.939	383
	Mod	87.09	12.91	0.894	0.871	0.892	180	94.14	5.86	0.947	0.941	0.942	386
	Max	90.27	16.98	0.908	0.903	0.902	397	94.24	12.61	0.947	0.942	0.943	396
	SD	1.66	1.66	0.013	0.017	0.016	110.51	1.56	1.56	0.014	0.015	0.016	92.22
	Avg	88.06	11.94	0.890	0.881	0.882	178.30	93.13	6.87	0.937	0.931	0.932	320.07
D ${}_{5}$	Min	78.05	6.26	0.809	0.781	0.773	33	92.85	4.37	0.934	0.929	0.929	138
	Q ${}_{1}$	92.08	6.55	0.924	0.921	0.921	165	95.03	4.67	0.953	0.950	0.951	187.25
	Med	93.25	6.75	0.935	0.932	0.932	206.50	95.23	4.77	0.955	0.952	0.953	215.50
	Q ${}_{3}$	93.45	7.92	0.937	0.934	0.935	272.75	95.33	4.97	0.956	0.953	0.954	255.75
	Mod	93.55	6.45	0.938	0.935	0.935	165	95.03	4.97	0.956	0.950	0.953	187
	Max	93.74	21.95	0.940	0.937	0.937	395	95.63	7.15	0.959	0.956	0.956	397
	SD	3.02	3.02	0.025	0.030	0.031	80.84	0.59	0.59	0.005	0.006	0.006	74.00
	Avg	92.09	7.91	0.925	0.921	0.921	217.53	95.08	4.92	0.954	0.950	0.951	237.60
D ${}_{6}$	Min	85.80	8.34	0.879	0.858	0.858	64	94.84	3.77	0.949	0.948	0.948	281
	Q ${}_{1}$	90.19	9.16	0.903	0.902	0.902	150.75	95.66	4.07	0.957	0.956	0.956	687
	Med	90.47	9.53	0.907	0.905	0.904	270	95.83	4.17	0.959	0.958	0.958	771
	Q ${}_{3}$	90.84	9.81	0.911	0.909	0.909	551	95.93	4.34	0.960	0.959	0.959	790
	Mod	90.37	9.63	0.912	0.904	0.906	148	95.83	4.17	0.959	0.958	0.958	776
	Max	91.66	14.20	0.919	0.917	0.916	849	96.23	5.16	0.963	0.962	0.962	850
	SD	1.26	1.26	0.009	0.013	0.013	260.57	0.32	0.32	0.003	0.003	0.003	143.85
	Avg	90.20	9.80	0.905	0.902	0.902	372.20	95.75	4.25	0.958	0.957	0.957	708.43
D ${}_{7}$	Min	90.57	5.56	0.914	0.906	0.907	144	96.52	2.98	0.965	0.965	0.965	416
	Q ${}_{1}$	92.58	6.48	0.926	0.926	0.926	316.25	96.72	3.18	0.967	0.967	0.967	720
	Med	93.25	6.75	0.934	0.932	0.932	363	96.82	3.18	0.968	0.968	0.968	792.50
	Q ${}_{3}$	93.52	7.43	0.937	0.935	0.935	584	96.82	3.28	0.968	0.968	0.968	817
	Mod	93.55	6.45	0.938	0.935	0.935	341	96.72	3.28	0.967	0.967	0.967	720
	Max	94.44	9.43	0.947	0.944	0.944	846	97.02	3.48	0.970	0.970	0.970	848
	SD	0.71	0.71	0.007	0.007	0.007	196.16	0.10	0.10	0.001	0.001	0.001	101.29
	Avg	93.01	6.99	0.932	0.930	0.930	453.83	96.80	3.20	0.968	0.968	0.968	747.53

Table 11

A comparative study based on the classification rate of the six proposed approaches

	The six proposed approaches (classification rate %)						Statistics
Data set	SVM $+$ SLS	NB $+$ SLS	$k$ -NN $+$ SLS	BN $+$ SLS	RT $+$ SLS	RF $+$ SLS	Min	Med	Max	SD	Avg
D ${}_{1}$	90.48	91.58	89.52	99.95	97.66	100	89.52	94.62	100	4.87	94.87
D ${}_{2}$	65.88	91.60	93.69	93.55	89.49	94.81	65.88	92.58	94.81	11.08	88.17
D ${}_{3}$	77.31	66.82	79.66	64.66	79.56	79.87	64.66	78.44	79.87	6.99	74.65
D ${}_{4}$	61.04	85.49	90.24	90.59	88.06	93.13	61.04	89.15	93.13	11.90	84.76
D ${}_{5}$	81.27	88.11	93.12	87.11	92.09	95.08	81.27	90.10	95.08	5.03	89.46
D ${}_{6}$	63.16	91.85	93.17	94.02	90.20	95.75	63.16	92.51	95.75	12.33	88.03
D ${}_{7}$	81.25	92.32	94.45	93.14	93.01	96.80	81.25	93.08	96.80	5.42	91.83
Avg										8.23	87.40

Table 12

A comparative study according to the number of selected attributes

Initial data set		Number of good attributes NA						Statistics
Data set	Attributes	SVM $+$ SLS	NB $+$ SLS	$k$ -NN $+$ SLS	BN $+$ SLS	RT $+$ SLS	RF $+$ SLS	Min	Med	Max	SD	Avg
D ${}_{1}$	10	4	5	4	4	5	6	4	4.50	6	0.82	4.67
D ${}_{2}$	454	136	233	433	388	251	378	136	314.50	433	114.23	303.17
D ${}_{3}$	30	17	12	18	15	16	19	12	16.50	19	2.48	16.17
D ${}_{4}$	397	86	166	334	357	178	320	86	249	357	111.32	240.17
D ${}_{5}$	397	150	350	222	313	218	238	150	230	350	71.98	248.50
D ${}_{6}$	851	290	378	825	658	372	708	290	518	825	219.24	538.50
D ${}_{7}$	851	270	664	628	611	454	748	270	619.50	748	172.44	562.50
Avg											98.93	273.38

The optimal solutions (OP) found by the third approach (Ap ${}_{3}$ : k-NN $+$ SLS with the probability $wp_{({k}\text{-NN}+\text{SLS})}=$ 0.6) and by the fourth approach (Ap ${}_{4}$ : BN $+$ SLS with the probability $wp_{(\text{BN}+\text{SLS})}=$ 0.6) are presented in Table 9. In the $k$ -NN $+$ SLS approach, the number of the nearest neighbors $k=$ {7, 1, 1, 1, 1, 1, 1} give respectively the best accuracy for the datasets: {D ${}_{1}$ , D ${}_{2}$ , D ${}_{3}$ , D ${}_{4}$ , D ${}_{5}$ , D ${}_{6}$ , D ${}_{7}$ }, and the Euclidean distance was used as the distance measure.

Table 10 illustrates the optimal solutions (OP) found by the fifth approach (Ap ${}_{5}$ : RT $+$ SLS with the probability $wp_{(\text{RT}+\text{SLS})}=$ 0.6) and by the sixth approach (Ap ${}_{6}$ : RF $+$ SLS with the probability $wp_{(\text{RF}+\text{SLS})}=$ 0.6).

Table 11 is derived from the three preceding tables (i.e. Tables 8–10), which represents a comparative study based on the classification rate (%) of the six approaches proposed for the seven datasets. The best results are shown in bold.

The empirical results in Table 11 show that the Ap ${}_{6}$ : RF $+$ SLS approach gives the best classification rate among the six approaches proposed for all the datasets used in this study {(Ap ${}_{6}$ : 100%, D ${}_{1}$ ), (Ap ${}_{6}$ : 94.81%, D ${}_{2}$ ), (Ap ${}_{6}$ : 79.87%, D ${}_{3}$ ), (Ap ${}_{6}$ : 93.13%, D ${}_{4}$ ), (Ap ${}_{6}$ : 95.08%, D ${}_{5}$ ), (Ap ${}_{6}$ : 95.75%, D ${}_{6}$ ), (Ap ${}_{6}$ : 96.80%, D ${}_{7}$ )}. Therefore, the best approach for classifying Web services among the other proposed approaches is the Ap ${}_{6}$ : RF $+$ SLS approach with probability $wp_{(\text{RF}+\text{SLS})}=$ 0.6.

Table 12 shows the number of the relevant attributes (the correct attributes) resulting from the application of the six proposed approaches applied to the seven datasets (D ${}_{1}$ , D ${}_{2}$ , D ${}_{3}$ , D ${}_{4}$ , D ${}_{5}$ , D ${}_{6}$ , and D ${}_{7}$ ). The best results are shown in bold.

The empirical results presented in Table 12 show a significant reduction in the number of attributes (i.e. the characteristics representing the Web service) for each dataset (D ${}_{1}$ , D ${}_{2}$ , …, D ${}_{7}$ ) at an estimated average rate (Avg) of: {Avg (D ${}_{1}$ ) $=$ 4.67, Avg (D ${}_{2}$ ) $=$ 303.17, Avg (D ${}_{3}$ ) $=$ 16.17, Avg (D ${}_{4}$ ) $=$ 240.17, Avg (D ${}_{5}$ ) $=$ 248.5, Avg (D ${}_{6}$ ) $=$ 538.50, and Avg (D ${}_{7}$ ) $=$ 562.50}, compared to the number of initial attributes of the seven datasets. Moreover, the comparison between the six approaches proposed in terms of the number of selected attributes clearly shows that these six approaches give the best classification rate (as well as: Re, Pr, Re, and FM) with a small set of attributes. In general, the Ap ${}_{1}$ : SVM $+$ SLS approach gives a smaller number of attributes compared to other approaches. Reducing the attributes number inevitably reduces the size of the dataset and therefore greatly increases the performance and the efficiency of the classifiers (in terms of accuracy).

Table 13 summarizes the main relevant attributes (good attributes) found by the proposed approaches for each dataset D ${}_{i}$ ( $i=1,\ldots,7$ ).

Table 13

The best attributes for each dataset D ${}_{i}$ ( $i=1,\ldots,7$ )

Data set	Number of selected attributes	The relevant attributes ranked in ascending order
D ${}_{1}$	4	$a_{2},a_{7},a_{9},a_{10}$
D ${}_{2}$	10	$a_{1},a_{7},a_{14},a_{15},a_{19},a_{22},a_{24},a_{27},a_{28},a_{31}$
D ${}_{3}$	10	$a_{7},a_{8},a_{11},a_{12},a_{13},a_{15},a_{19},a_{21},a_{22},a_{23}$
D ${}_{4}$	10	$a_{9},a_{17},a_{18},a_{19},a_{21},a_{22},a_{23},a_{25},a_{29},a_{31}$
D ${}_{5}$	10	$a_{18},a_{19},a_{21},a_{22},a_{23},a_{25},a_{29},a_{31},a_{32},a_{33}$
D ${}_{6}$	10	$a_{1},a_{2},a_{4},a_{7},a_{8},a_{9},a_{10},a_{11},a_{14},a_{15}$
D ${}_{7}$	10	$a_{1},a_{7},a_{11},a_{14},a_{15},a_{17},a_{19},a_{22},a_{24},a_{28}$

Table 14

A comparative study according to the average calculation time (sec) of each approach

Data set	SVM $+$ SLS	NB $+$ SLS	$k$ -NN $+$ SLS	BN $+$ SLS	RT $+$ SLS	RF $+$ SLS	Min	Max	SD	Avg
	The calculation time in seconds CT (sec)						Statistics
D ${}_{1}$	105.38	116.92	115.70	113.86	123.15	110.51	105.38	123.15	6.02	114.25
D ${}_{2}$	2716.97	2783.28	2848.61	2731.51	3096.25	2627.04	2627.04	3096.25	162.42	2800.61
D ${}_{3}$	209.43	215.41	213.26	217.72	222.74	229.99	209.43	229.99	7.33	218.09
D ${}_{4}$	2229.22	2417.37	2504.92	2257.97	2420.57	2309.83	2229.22	2504.92	107.63	2356.65
D ${}_{5}$	2350.56	2396.43	2448.76	2361.19	2506.72	2443.12	2350.56	2506.72	59.48	2417.80
D ${}_{6}$	4501.51	5154.79	5311.33	4993.28	5255.07	4877.31	4501.51	5311.33	299.36	5015.55
D ${}_{7}$	3913.63	5129.12	5191.43	5064.42	5472.08	4580.36	3913.63	5472.08	559.72	4891.84
Avg									171.71	2544.97

Figure 1.

Box plot for the dataset D ${}_{1}$ : QWS Dataset and the dataset D ${}_{2}$ : Text.

Figure 2.

Box plot for the dataset D ${}_{3}$ : OntImp and the dataset D ${}_{4}$ : SynSig.

Figure 3.

Box plot for the dataset D ${}_{5}$ : SemSig and the dataset D ${}_{6}$ : TextSynSig.

Each of the proposed approaches takes a certain amount of calculation time to find optimal solutions depending on the size and number of attributes of the dataset, on the one hand, and on the other hand, depending on the speed of the computer and its operating system. Table 14 shows the average calculation time (i.e. 30 calculation times, see Table 3 parameter P ${}_{1}$ ) in seconds to find the optimal solutions for each of the six approaches proposed in this study. Each approach has been validated and tested on seven different datasets. The best results are shown in bold.

The box plots (Q ${}_{1}$ , Med, Q ${}_{3}$ , and the outlier values: represented by the small circles) of Figs 1–4 illustrate the distribution of the classification rates of the six proposed approaches (on the 30 executions) for each dataset.

Figure 4.

Box plot for the dataset D ${}_{7}$ : TextSemSig.

The box plots (Figs 1–4) clearly show that the sixth approach (Ap ${}_{6}$ : RF $+$ SLS) gave a better result (good result) in terms of classification rates compared to other proposed approaches. Moreover, the approach (Ap ${}_{1}$ : SVM $+$ SLS) gave the widest interquartile space IQR (i.e. the distance between the 1 ${}^{\text{st}}$ and the 3 ${}^{\text{rd}}$ quartile) in all datasets D ${}_{i}$ ( $i=1,\ldots,7$ ). In other words, the SVM classifier has significantly improved when combined with the SLS meta-heuristic compared to the other approaches.

6.7 Comparison and validation of the proposed approaches

In order to compare and validate the six proposed approaches, four comparison phases based on classification rates were performed: the first phase, comparison of proposed approaches with SVM, NB, $k$ -NN, BN, RT, and RF. The second phase, the use of the Ranker Search Method RSM [52] associated with the basic classifiers. The third phase, the use of 24 learning WEKA methods [52], and the fourth phase, the use of some approaches from previous work. The details of these comparisons are presented below.

6.7.1 The first (1 ${}^{\text{st}}$ ) phase of comparison

During this phase, the comparison is made between the proposed approaches (hybrid classifiers) and their basic classifiers (SVM, NB, $k$ -NN, BN, RT, and RF) validated and tested on 7 data sets D ${}_{i}$ ( $i=1,\ldots,7$ ). More precisely, the comparison is made between the pairs of the following classifiers: {(SVM, SVM $+$ SLS), (NB, NB $+$ SLS), ( $k$ -NN, $k$ -NN $+$ SLS), (BN, BN $+$ SLS), (RT, RT $+$ SLS), and (RF, RF $+$ SLS)}. Table 15 shows the results obtained from the first comparison phase (the best results are shown in bold).

Table 15
The first phase of comparison based on the classification rate (%)

	1 ${}^{\text{st}}$ Versus		2 ${}^{\text{nd}}$ Versus		3 ${}^{\text{rd}}$ Versus		4 ${}^{\text{th}}$ Versus		5 ${}^{\text{th}}$ Versus		6 ${}^{\text{th}}$ Versus
Data set	SVM	SVM $+$ SLS	NB	NB $+$ SLS	$k$ -NN	$k$ -NN $+$ SLS	BN	BN $+$ SLS	RT	RT $+$ SLS	RF	RF $+$ SLS
D ${}_{1}$	85.44	90.48	81.87	91.58	77.47	89.52	99.73	99.95	94.51	97.66	100	100
D ${}_{2}$	55.81	65.88	90.37	91.60	93.25	93.69	93.35	93.55	87.09	89.49	94.44	94.81
D ${}_{3}$	75.37	77.31	60.68	66.82	79.64	79.66	60.68	64.66	79.64	79.56	79.84	79.87
D ${}_{4}$	36.25	61.04	84.51	85.49	90.07	90.24	90.37	90.59	86.99	88.06	92.25	93.13
D ${}_{5}$	72.69	81.27	85.8088.11		92.45	93.12	86.40	87.11	90.67	92.09	94.44	95.08
D ${}_{6}$	45.58	63.16	89.97	91.85	93.15	93.17	93.35	94.02	85.60	90.20	95.63	95.75
D ${}_{7}$	67.43	81.25	91.96	92.32	93.84	94.45	91.66	93.14	90.37	93.01	96.72	96.80
Min	36.25	61.04	60.68	66.82	77.47	79.66	60.68	64.66	79.64	79.56	79.84	79.87
Med	67.43	77.31	85.80	91.58	92.45	93.12	91.66	93.14	87.09	90.20	94.44	95.08
Max	85.44	90.48	91.96	92.32	93.84	94.45	99.73	99.95	94.51	97.66	100	100
SD	17.51	11.09	10.73	09.17	06.96	05.14	12.67	11.41	04.70	05.56	06.41	6.43
Avg	62.65	74.34	83.59	86.82	88.55	90.55	87.93	89.00	87.84	90.01	93.33	93.63

In general, the experimental results presented in Table 15 showed a significant increase in the classification rate in each of the proposed hybrid classifiers compared to the basic classifiers, with a success rate of 97.62% (i.e. 41 classification rate out of 42: 41/42), except the case of the RT method validated on dataset D ${}_{3}$ : OntImp in which the accuracy rate did not improve (i.e. the RT method with an Accuracy rate of 79.64% is better than the Ap ${}_{5}$ : RT $+$ SLS approach validated on dataset D ${}_{3}$ : OntImp with an Accuracy rate of 79.56%). By observing the 42 classification rates resulting from the six proposed approaches, the first approach (Ap ${}_{1}$ : SVM $+$ SLS, SVM) showed a significant increase in the values of the classification rates resulting from the seven sets of data compared to the rest of the other approaches. Moreover, we note that all values of the average classification rates (Avg.) for the six proposed approaches have been improved {(Ap ${}_{1}$ : SVM $+$ SLS $=$ 74.34%), (Ap ${}_{2}$ : NB $+$ SLS $=$ 86.82%), Ap ${}_{3}$ : ( $k$ -NN $+$ SLS $=$ 90.55%), Ap ${}_{4}$ : (BN $+$ SLS $=$ 89.00%), (Ap ${}_{5}$ : RT $+$ SLS $=$ 90.01%), and Ap ${}_{6}$ : (RF $+$ SLS $=$ 93.63%)}. The results obtained in Table 15 clearly show that the six proposed optimization approaches are much better than the basic chosen methods.

6.7.2 The second (2

{}^{\text{nd}}

) phase of comparison

In the second (2 ${}^{\text{nd}}$ ) comparison phase, we chose to compare each proposed approach with each classifier associated with the WEKA Ranker Search Method [52] validated and tested on 7 datasets (D ${}_{1}$ , D ${}_{2}$ , D ${}_{3}$ , D ${}_{4}$ , D ${}_{5}$ , D ${}_{6}$ , and D ${}_{7}$ ). The Ranker Search Method (RSM) [52] is an attribute selection method that allows the attributes to be ordered according to their individual evaluation value, this method is divided into two parts: the evaluator of the attribute value based on the gain ratio with respect to the class (GainRatioAttributeEval), and the search method for choosing a short list of attributes (a fixed threshold or a number of attributes to keep). More precisely, the comparison is made between the pairs of the following classifiers: {(SVM $+$ RSM, SVM $+$ SLS), (NB $+$ RSM, NB $+$ SLS), ( $k$ -NN $+$ RSM, $k$ -NN $+$ SLS), (BN $+$ RSM, BN $+$ SLS), (RT $+$ RSM, RT $+$ SLS), and (RF $+$ RSM, RF $+$ SLS)}. The results of this comparison phase are illustrated in Table 16 (the best results are shown in bold).

Table 16
The second phase of comparison based on the classification rate (%)

	1 ${}^{\text{st}}$ Versus		2 ${}^{\text{nd}}$ Versus		3 ${}^{\text{rd}}$ Versus		4 ${}^{\text{th}}$ Versus		5 ${}^{\text{th}}$ Versus		6 ${}^{\text{th}}$ Versus
Data set	SVM $+$ RSM	SVM $+$ SLS	NB $+$ RSM	NB $+$ SLS	$k$ -NN $+$ RSM	$k$ -NN $+$ SLS	BN $+$ RSM	BN $+$ SLS	RT $+$ RSM	RT $+$ SLS	RF $+$ RSM	RF $+$ SLS
D ${}_{1}$	85.71	90.48	82.42	91.58	87.36	89.52	100	99.95	96.70	97.66	100	100
D ${}_{2}$	62.26	65.88	89.08	91.60	93.45	93.69	92.65	93.55	88.48	89.49	91.66	94.81
D ${}_{3}$	69.31	77.31	61.07	66.82	74.98	79.66	62.86	64.66	70.31	79.56	76.86	79.87
D ${}_{4}$	50.25	61.04	66.04	85.49	87.98	90.24	88.18	90.59	73.49	88.06	89.28	93.13
D ${}_{5}$	76.86	81.27	85.30	88.11	86.20	93.12	86.79	87.11	87.39	92.09	89.18	95.08
D ${}_{6}$	59.09	63.16	88.28	91.85	92.95	93.17	93.15	94.02	89.77	90.20	93.94	95.75
D ${}_{7}$	75.07	81.25	91.06	92.32	89.18	94.45	91.56	93.14	90.37	93.01	96.62	96.80
Min	50.25	61.04	61.07	66.82	74.98	79.66	62.86	64.66	70.31	79.56	76.86	79.87
Med	69.31	77.31	85.30	91.58	87.98	93.12	91.56	93.14	88.48	90.20	91.66	95.08
Max	85.71	90.48	91.06	92.32	93.45	94.45	100	99.95	96.70	97.66	100	100
SD	12.04	11.09	11.97	09.17	06.15	05.14	11.82	11.41	09.61	05.56	07.39	6.43
Avg	68.36	74.34	80.46	86.82	87.44	90.55	87.88	89.00	85.22	90.01	91.08	93.63

Figure 5.

Histogram of comparison for the dataset D ${}_{1}$ : QWS Dataset and the dataset D ${}_{2}$ : Text.

The results in Table 16 indicate that 40 of the 42 classification rates of the proposed approaches have improved compared to the basic methods combined with RSM, with a success rate of 95.24% (i.e. 40 classification rate out of 42: 40/42), while one case has remained unchanged (Ap ${}_{6}$ : RF $+$ SLS $=$ 100% and RF $+$ RSM $=$ 100% were validated on the same dataset D ${}_{1}$ ) and another did not improve (Ap ${}_{4}$ : BN $+$ SLS $=$ 99.95% and BN $+$ RSM $=$ 100% were validated on the same dataset D ${}_{1}$ ). Moreover, we note that all values of the average classification rates (Avg.) for the six proposed approaches have been improved {(Ap ${}_{1}$ : SVM $+$ SLS $=$ 74.34%), (Ap ${}_{2}$ : NB $+$ SLS $=$ 86.82%), (Ap ${}_{3}$ : $k$ -NN $+$ SLS $=$ 90.55%), (Ap ${}_{4}$ : BN $+$ SLS $=$ 89.00%), (Ap ${}_{5}$ : RT $+$ SLS $=$ 90.01%), and (Ap ${}_{6}$ : RF $+$ SLS $=$ 93.63%)}. The results obtained in Table 16 clearly show that the six proposed optimization approaches are much better than the basic methods combined with the RSM attribute selection method of the WEKA software.

Figure 6.

Histogram of comparison for the dataset D ${}_{3}$ : OntImp and the dataset D ${}_{4}$ : SynSig.

Figure 7.

Histogram of comparison for the dataset D ${}_{5}$ : SemSig and the dataset D ${}_{6}$ : TextSynSig.

Figure 8.

Histogram of comparison for the dataset D ${}_{7}$ : TextSemSig.

The histograms of Figs 5–8 represents a comparison based on the classification rates between three types of classifiers {the basic classifiers, the basic classifiers combined with RSM, and the basic classifiers combined with SLS (the six proposed approaches)} validated for each dataset D ${}_{i}$ ( $i=1,\ldots,7$ ).

According to the results presented in graphs (Figs 5–8), it is clear that the proposed approaches (SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS) are much better in terms of classification rates than the basic classifiers combined with RSM (SVM $+$ RSM, NB $+$ RSM, $k$ -NN $+$ RSM, BN $+$ RSM, RT $+$ RSM, and RF $+$ RSM) and also for basic classifiers (SVM, NB, $k$ -NN, BN, RT, and RF), and this for all datasets (D ${}_{1}$ , D ${}_{2}$ , …, D ${}_{7}$ ). The results obtained are very encouraging and interesting and demonstrate the advantages of the proposed approaches for the supervised classification of Web services, in particular the use of the SLS meta-heuristic for the selection of good attributes (the relevant attributes).

6.7.3 The third (3

{}^{\text{rd}}

) phase of comparison

In the third (3 ${}^{\text{rd}}$ ) comparison phase, a list of 24 supervised classification methods of the WEKA software [52] was chosen and used with their predefined parameters. In this case, the comparison is made between the six proposed approaches and the 24 WEKA classification methods. These methods are presented in Table 17.

Table 17
List of 24 supervised classification methods of WEKA [52]

Id	Group	WEKA methods	Id	Group	WEKA methods
1	Functions	logistic (L)	13	Meta	MultiClassClassifer (MCC)
2	Functions	RBFNetwork (RBFN)	14	Meta	MultiScheme (MS)
3	Functions	SMO	15	Meta	Vote (V)
4	Functions	MLPClassifier (MLPC)	16	Lazy	KStar (KS)
5	Functions	RBFClassifier (RBFC)	17	Lazy	LWL
6	Bayes	NaiveBayesMultinominalText (NBMT)	18	Lazy	RseslibKnn (RK)
7	Bayes	NaiveBayesUpdateable (NBU)	19	Misc	CHIRP
8	Meta	AdaBoostM1 (ABM1)	20	Misc	InputMappedClassifier (IMC)
9	Meta	CVParameterSelection (CVPS)	21	Rules	ConjunctiveRule (CR)
10	Meta	MultiClassClassifierUpdateable (MCCU)	22	Rules	ZeroR (ZR)
11	Meta	AttributeSelectedClassifier (ASC)	23	Trees	DecisionStump (DS)
12	Meta	RandomizableFiltredClassifier (RFC)	24	Trees	HoeffdingTree (HT)

Tables 18 and 19 show respectively the results of the descending comparison (i.e. R. From 1 to 30) of the classification rates (Acc %) between the six proposed approaches and the list of 24 supervised classification methods of WEKA [52] validated respectively on the datasets (D ${}_{1}$ , D ${}_{2}$ , D ${}_{3}$ , D ${}_{4}$ ) and (D ${}_{5}$ , D ${}_{6}$ , D ${}_{7}$ ).

Table 18

Top ranking (R) of classification methods for datasets: D ${}_{1}$ , D ${}_{2}$ , D ${}_{3}$ , and D ${}_{4}$

Dataset D ${}_{1}$ : QWS dataset			Dataset D ${}_{2}$ : Text			Dataset D ${}_{3}$ : OntImp			Dataset D ${}_{4}$ : SynSig
R	Method	Acc %	R	Method	Acc %	R	Method	Acc %	R	Method	Acc %
1	RF $+$ SLS	100	1	RF $+$ SLS	94.81	1	RF $+$ SLS	79.87	1	SMO	94.04
2	BN $+$ SLS	99.95	2	SMO	94.04	2	k-NN $+$ SLS	79.66	2	L	93.74
3	ASC	99.73	3	KS	93.94	3	SMO	79.64	3	MCC	93.74
4	RT $+$ SLS	97.66	4	k-NN $+$ SLS	93.69	4	RFC	79.64	4	RF $+$ SLS	93.13
5	L	93.13	5	MCCU	93.64	5	RT $+$ SLS	79.56	5	MCCU	92.35
6	NB $+$ SLS	91.58	6	BN $+$ SLS	93.55	6	RBFN	79.44	6	CHIRP	92.35
7	SVM $+$ SLS	90.48	7	CHIRP	93.25	7	L	78.85	7	KS	91.76
8	k-NN $+$ SLS	89.52	8	RK	92.55	8	KS	78.75	8	RBFN	91.26
9	CHIRP	89.29	9	NB $+$ SLS	91.60	9	MCC	77.86	9	RK	90.96
10	HT	87.64	10	RBFN	90.37	10	SVM $+$ SLS	77.31	10	BN $+$ SLS	90.59
11	RBFN	86.81	11	NBU	90.37	11	MLPC	75.67	11	k-NN $+$ SLS	90.24
12	SMO	86.54	12	MCC	90.17	12	CHIRP	75.27	12	RT $+$ SLS	88.06
13	RK	85.99	13	L	89.97	13	ASC	75.07	13	MLPC	85.80
14	MLPC	85.71	14	RT $+$ SLS	89.49	14	MCCU	73.78	14	NB $+$ SLS	85.49
15	MCC	85.44	15	MLPC	82.92	15	RBFC	69.81	15	NBU	84.51
16	KS	82.69	16	ASC	80.73	16	NB $+$ SLS	66.82	16	HT	84.51
17	RBFC	78.02	17	RFC	73.09	17	LWL	66.53	17	ASC	79.15
18	LWL	77.47	18	RBFC	71.40	18	BN $+$ SLS	64.66	18	RBFC	73.78
19	MCCU	76.37	19	SVM $+$ SLS	65.88	19	RK	62.16	19	RFC	66.93
20	RFC	75.00	20	HT	60.97	20	NBU	60.68	20	SVM $+$ SLS	61.04
21	ABM1	60.44	21	CR	57.30	21	HT	60.68	21	LWL	47.77
22	DS	60.44	22	LWL	55.91	22	ABM1	57.30	22	ABM1	43.40
23	CR	60.44	23	ABM1	55.91	23	DS	57.30	23	DS	43.40
24	NBU	81.87	24	DS	55.91	24	CR	57.30	24	CR	42.70
25	NBMT	32.97	25	NBMT	36.25	25	NBMT	36.25	25	NBMT	36.25
26	CVPS	32.97	26	CVPS	36.25	26	CVPS	36.25	26	CVPS	36.25
27	IMC	32.97	27	IMC	36.25	27	IMC	36.25	27	IMC	36.25
28	MS	32.97	28	MS	36.25	28	MS	36.25	28	MS	36.25
29	ZR	32.97	29	ZR	36.25	29	ZR	36.25	29	ZR	36.25
30	V	32.97	30	V	36.25	30	V	36.25	30	V	36.25
	SD	23.29		SD	22.59		SD	16.17		SD	23.74
	Avg	74.00		Avg	72.30		Avg	64.37		Avg	70.61

Table 19

Top ranking (R) of classification methods for datasets: D ${}_{5}$ , D ${}_{6}$ , and D ${}_{7}$

Dataset D ${}_{5}$ : SemSig			Dataset D ${}_{6}$ : TextSynSig			Dataset D ${}_{7}$ : TextSemSig
R	Method	Acc %	R	Method	Acc %	R	Method	Acc %
1	SMO	96.92	1	RF $+$ SLS	95.75	1	RF $+$ SLS	96.80
2	RF $+$ SLS	95.08	2	SMO	95.73	2	SMO	96.52
3	L	93.84	3	MCCU	94.54	3	KS	95.03
4	MCCU	93.64	4	RK	94.44	4	MCCU	95.03
5	k-NN $+$ SLS	93.12	5	KS	94.34	5	k-NN $+$ SLS	94.45
6	KS	93.05	6	L	94.04	6	RK	94.34
7	RK	92.75	7	BN $+$ SLS	94.02	7	L	94.04
8	MCC	92.25	8	k-NN $+$ SLS	93.17	8	BN $+$ SLS	93.14
9	RT $+$ SLS	92.09	9	CHIRP	92.65	9	RT $+$ SLS	93.01
10	CHIRP	89.28	10	MCC	92.55	10	NB $+$ SLS	92.32
11	RBFN	88.58	11	NB $+$ SLS	91.85	11	NBU	91.96
12	NB $+$ SLS	88.11	12	RBFN	91.36	12	HT	91.96
13	MLPC	87.69	13	RT $+$ SLS	90.20	13	CHIRP	91.56
14	BN $+$ SLS	87.11	14	NBU	89.97	14	RBFN	91.06
15	RFC	87.09	15	ASC	82.03	15	MCC	90.07
16	HT	85.80	16	MLPC	81.63	16	ASC	87.39
17	NBU	85.80	17	RBFC	73.39	17	MLPC	86.00
18	ASC	84.51	18	RFC	67.23	18	SVM $+$ SLS	81.25
19	SVM $+$ SLS	81.27	19	SVM $+$ SLS	63.16	19	RFC	81.23
20	RBFC	74.98	20	HT	58.59	20	RBFC	74.38
21	CR	59.88	21	CR	57.30	21	CR	59.88
22	ABM1	57.80	22	LWL	55.91	22	DS	57.80
23	LWL	57.80	23	DS	55.91	23	ABM1	57.80
24	DS	57.80	24	ABM1	55.91	24	LWL	57.80
25	NBMT	36.25	25	NBMT	36.25	25	NBMT	36.25
26	CVPS	36.25	26	CVPS	36.25	26	CVPS	36.25
27	IMC	36.25	27	IMC	36.25	27	IMC	36.25
28	MS	36.25	28	MS	36.25	28	MS	36.25
29	ZR	36.25	29	ZR	36.25	29	ZR	36.25
30	V	36.25	30	V	36.25	30	V	36.25
	SD	22.47		SD	23.09		SD	23.21
	Avg	74.46		Avg	72.44		Avg	75.41

According to the results presented in both tables: (Tables 18 and 19), it is clear that the validated proposed approaches on the seven datasets are much better compared to the 24 WEKA methods [52]. For example, the Ap ${}_{6}$ : RF $+$ SLS approach is ranked first place (among a list of 24 methods supervised WEKA) in the following datasets: D ${}_{1}$ : QWS Dataset, D ${}_{2}$ : Text, D ${}_{3}$ : OntImp, D ${}_{6}$ : TextSynSig, and D ${}_{7}$ : TextSemSig, and ranked fourth in D ${}_{4}$ : SynSig and second in D ${}_{5}$ : SemSig. Moreover, the Ap ${}_{4}$ : BN $+$ SLS approach is ranked 2 ${}^{\text{nd}}$ position in the dataset D ${}_{1}$ : QWS Dataset and the Ap ${}_{3}$ : k-NN $+$ SLS approach is ranked 3 ${}^{\text{rd}}$ in the dataset D ${}_{3}$ : OntImp.

6.7.4 The fourth (4

{}^{\text{th}}

) phase of comparison

In the fourth (4 ${}^{\text{th}}$ ) comparison phase, we present a comparative study between the six proposed approaches with some approaches presented in the related works section. This comparative study has been presented in Table 20 (Where, R: Ranking).

Table 20
Comparison of proposed approaches and other approaches presented in related works

R	Approach: Dataset	Acc.	R	Approach: Dataset	Acc.	R	Approach: Dataset	Acc.
1	RF $+$ SLS: D ${}_{1}$	100	24	NB $+$ SLS: D ${}_{7}$	92.32	47	TS: D ${}_{1}$ [32]	82.45
2	BN $+$ SLS: D ${}_{1}$	99.95	25	RT $+$ SLS: D ${}_{5}$ 92.09		48	SVM-SMO: D ${}_{1}$ [33]	81.37
3	CNBP: D ${}_{1}$ [56]	98.40	26	MEC: 3738WS [43]	92.00	49	MB: D ${}_{1}$ [32]	81.36
4	MLP-GA: D ${}_{1}$ [35]	97.81	27	NB $+$ SLS: D ${}_{6}$	91.85	50	SVM $+$ SLS: D ${}_{5}$	81.27
5	RT $+$ SLS: D ${}_{1}$	97.66	28	NB $+$ SLS: D ${}_{2}$	91.60	51	SVM $+$ SLS: D ${}_{7}$	81.25
6	MLP-TS: D ${}_{1}$ [34]	97.53	29	NB $+$ SLS: D ${}_{1}$	91.58	52	FURIA: D ${}_{1}$ [33]	80.55
7	MLP-BPP: D ${}_{1}$ [34, 35]	96.99	30	FRONN $+$ GR: D ${}_{1}$ [40]	91.21	53	C4.5: OWLS-TC4 [53]	80.00
8	FRONN $+$ IG: D ${}_{1}$ [40]	96.98	31	TM: 600WS [38]	90.60	54	NB: 165WS [46]	80.00
9	RF $+$ SLS: D ${}_{7}$	96.80	32	BN $+$ SLS: D ${}_{4}$	90.59	55	RF $+$ SLS: D ${}_{3}$	79.87
10	RF $+$ SLS: D ${}_{6}$	95.75	33	SVM $+$ SLS: D ${}_{1}$	90.48	56	BN $+$ SLS: D ${}_{3}$	79.86
11	MLP-LM: D ${}_{1}$ [34]	95.34	34	k-NN $+$ SLS: D ${}_{4}$	90.24	57	k-NN $+$ SLS: D ${}_{3}$	79.66
12	RF $+$ SLS: D ${}_{5}$	95.08	35	RT $+$ SLS: D ${}_{6}$	90.20	58	RT $+$ SLS: D ${}_{3}$	79.56
13	ME: OWLS-TC3 [45]	95.00	36	k-NN $+$ SLS: D ${}_{1}$	89.52	59	RIDOR: D ${}_{1}$ [33]	78.63
14	RF $+$ SLS: D ${}_{2}$	94.81	37	RT $+$ SLS: D ${}_{2}$	89.49	60	NB: D ${}_{1}$ [35]	77.81
15	k-NN $+$ SLS: D ${}_{7}$	94.45	38	SN: 10184WS [55]	88.40	61	SVM $+$ SLS: D ${}_{3}$	77.31
16	BN $+$ SLS: D ${}_{6}$	94.02	39	NB $+$ SLS: D ${}_{5}$	88.11	62	k-NN: D ${}_{1}$ [33]	76.16
17	k-NN $+$ SLS: D ${}_{2}$	93.69	40	RT $+$ SLS: D ${}_{4}$	88.06	63	NB $+$ SLS: D ${}_{3}$	66.82
18	BN $+$ SLS: D ${}_{2}$	93.55	41	AB: 951WS [54]	87.39	64	SVM $+$ SLS: D ${}_{2}$	65.88
19	k-NN $+$ SLS: D ${}_{6}$	93.17	42	BN $+$ SLS: D ${}_{5}$	87.11	65	BN $+$ SLS: D ${}_{3}$	64.66
20	BN $+$ SLS: D ${}_{7}$	93.14	43	FRONN-FS: D ${}_{1}$ [40]	86.81	66	SVM $+$ SLS: D ${}_{6}$	63.16
21	RF $+$ SLS: D ${}_{4}$	93.13	44	NBC: D ${}_{1}$ [32]	85.62	67	J48: D ${}_{1}$ [48]	63.00
22	k-NN $+$ SLS: D ${}_{5}$	93.12	45	NB $+$ SLS: D ${}_{4}$	85.49	68	SVM $+$ SLS: D ${}_{4}$	61.04
23	RT $+$ SLS: D ${}_{7}$	93.01	46	AWSC: 235WS [16]	85.08	69	AR: 165WS [46]	30.91

Table 20 shows that the methods proposed gave good results in terms of classification rates compared to the results presented in the previous works. For example, the Ap ${}_{6}$ : RF $+$ SLS approach validated on dataset D ${}_{1}$ : QWS Dataset is ranked first (1 ${}^{\text{st}}$ ) with an Accuracy rate of 100%, and the Ap ${}_{4}$ : BN $+$ SLS approach validated on dataset D ${}_{1}$ : QWS Dataset is ranked second (2 ${}^{\text{nd}}$ ) with an Accuracy rate of 99.95%, and in fifth (5 ${}^{\text{th}}$ ) place comes the Ap ${}_{5}$ : RT $+$ SLS approach with an accuracy rate of 97.66% validated on dataset D ${}_{1}$ : QWS Dataset. In ninth (9 ${}^{\text{th}}$ ) place, tenth (10 ${}^{\text{th}}$ ), twelfth (12 ${}^{\text{th}}$ ) and fourteenth (14 ${}^{\text{th}}$ ), the Ap ${}_{6}$ : RF $+$ SLS approach had the following classification rates: 96.80%, 95.75%, 95.08%, and 94.81%, validated on the following datasets: {D ${}_{7}$ : TextSemSig, D ${}_{6}$ : TextSynSig, D ${}_{5}$ : SemSig, D ${}_{2}$ : Text}. The Ap ${}_{3}$ : $k$ -NN $+$ SLS approach with $k=$ 1 is ranked 15 ${}^{\text{th}}$ with an accuracy rate of 94.45% validated on dataset D ${}_{7}$ : TextSemSig, the Ap ${}_{4}$ : BN $+$ SLS approach is ranked 16 ${}^{\text{th}}$ with an accuracy rate of 94.02% validated on dataset D ${}_{6}$ : TextSynSig, the Ap ${}_{2}$ : NB $+$ SLS approach is ranked in 24 ${}^{\text{rd}}$ position with an accuracy rate of 92.32% validated on dataset D ${}_{7}$ : TextSemSig, and finally, the Ap ${}_{1}$ : SVM $+$ SLS approach is ranked in 33 ${}^{\text{rd}}$ position with an accuracy rate of 90.48% validated on dataset D ${}_{1}$ : QWS Dataset.

Note that the most approaches from related work are validate on the dataset D ${}_{1}$ : QWS Dataset (23 approaches), so the Fig. 9 presents a comparison between the approaches using the same data set D ${}_{1}$ : QWS Dataset.

Figure 9.

Comparative graph between the approaches using the dataset D ${}_{1}$ : QWS Dataset.

6.8 Analysis and discussion

The numerical results of the four phases of the previous comparisons are interesting and demonstrate the benefits of the proposed approaches for the Web services classification (see Tables 15 and 16, 18–20). These results showed that the proposed hybrid approaches {(SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS)} have given good classification rates. Therefore, the use of SLS meta-heuristic as a combinatorial optimization method that allows selection of the relevant attributes of the WSDL document. These relevant attributes facilitate the task of classifying these documents. The performed experiments showed that the $w p$ parameter has a huge impact on the SLS meta-heuristic to explore the search space in an optimal way and find the best solution in the neighborhood. According to this study, the attributes selection by the meta-heuristic SLS is very beneficial, this meta-heuristic associated with a supervised machine learning algorithm to improve the evaluations measures of the classifiers performance (Accuracy rate) and thus considerably reduce the attributes space (see Table 12) and reduce the dataset size. This reduction facilitates the process of publishing, discovering, and invoking Web services. Meta-heuristics is therefore very effective for classifying Web services into predetermined categories. Finally, the results of these experiments are promising and confirm the interest of using the meta-heuristics, especially the Stochastic Local Search (SLS) which has contributed to improve the quality of the solution to the Web services classification problem.

7. Conclusion

The classification of Web services is an important issue in Web service engineering where several machine learning techniques can be used to handle the classification task. In this paper, we focus on supervised classification techniques for classifying Web services. The technique permits to assign a new Web service (represented as a WSDL document) to its appropriate class chosen among a list of learning documents. This process helps in improving the speed of discovery process and the invocation of Web services (i.e. improve the response time). To this end, we propose several hybrid approaches for classifying Web services where a stochastic local search meta-heuristic (SLS) was used as a feature selection mechanism. The role of SLS is to select only a set of significant attributes before starting the classification process. Then the classification task is done by using a machine learning algorithm with 10-fold cross validation as an evaluation method for the generated models. This hybridization aims to enhance the classification rate. In this study, we consider six well-known supervised machine learning algorithms in the field of machine learning which are: SVM, NB, $k$ -NN, BN, RT, and RF. These algorithms are combined with SLS (SVM $+$ SLS, NB $+$ SLS, $k$ -NN $+$ SLS, BN $+$ SLS, RT $+$ SLS, and RF $+$ SLS) to build new optimized classifiers based on the best subsets of attributes found by SLS to essentially improve the classification rate (i.e. the objective function). The performance of the proposed approaches has been validated and tested on seven real data sets available on the Web (D ${}_{1}$ , D ${}_{2}$ , …, D ${}_{7}$ ) and compared with the six basic classifiers (SVM, NB, $k$ -NN, BN, RT, and RF), with the WEKA attribute selection method called Ranker Search Method (RSM) combined with the six basic classifiers, with 24 WEKA learning methods and with other approaches of previous work. The results were promising and showed the performance of the proposed approaches. These latters improved evaluation measures, specifically the classification rate. In perspective, we have several directions to improve this study. First introduce multiple meta-heuristics, especially genetic algorithms for the selection of good attributes, combined with supervised machine learning algorithms to improve their performance. It would be interested to study the impact of unsupervised machine learning algorithms combined with meta-heuristics for Web services classification.

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Improved machine learning classifiers combined with a stochastic local search for Web services classification

Abstract

Keywords

1. Introduction

2. Related works

Table 1 Related works approaches for Web services classification

4.1 Machine learning algorithms (supervised classification methods)

4.1.1 Support Vector Machine (SVM)

4.1.6 Random Forest (RF)

4.2 Optimization with the SLS meta-heuristic

5. Proposed approaches

5.2 The general form of a solution generated by SLS

5.3 The proposed optimization algorithm with SLS for attribute selection

6. Experimental results

Table 2 Implementation details for the proposed approaches

6.2 The parameters of the proposed approaches (parameters tuning)

6.3 Data sets used in this study

Table 4 The general description of QWS Dataset and the six versions of OWLS-TC ver. 2.2 [2, 24]

Table 5 The detailed description of QWS Dataset [2, 3, 4]

Table 6 The detailed description of the OWLS-TC ver. 2.2 [24, 25]

6.7.1 The first (1 st ) phase of comparison

Table 15 The first phase of comparison based on the classification rate (%)

Table 16 The second phase of comparison based on the classification rate (%)

Table 17 List of 24 supervised classification methods of WEKA [52]

Table 20 Comparison of proposed approaches and other approaches presented in related works

7. Conclusion

References

Table 1
Related works approaches for Web services classification

Table 2
Implementation details for the proposed approaches

Table 4
The general description of QWS Dataset and the six versions of OWLS-TC ver. 2.2 [2, 24]

Table 5
The detailed description of QWS Dataset [2, 3, 4]

Table 6
The detailed description of the OWLS-TC ver. 2.2 [24, 25]

6.7.1 The first (1 ${}^{\text{st}}$ ) phase of comparison

Table 15
The first phase of comparison based on the classification rate (%)

Table 16
The second phase of comparison based on the classification rate (%)

Table 17
List of 24 supervised classification methods of WEKA [52]

Table 20
Comparison of proposed approaches and other approaches presented in related works